TSTP Solution File: PUZ008-3 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : PUZ008-3 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 : Fri May 19 11:47:23 EDT 2023

% Result   : Unsatisfiable 3.31s 1.91s
% Output   : Refutation 3.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   44 (   9 unt;  11 typ;   0 def)
%            Number of atoms       :   97 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  842 (  66   ~;  64   |;   0   &; 712   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :   94 (   0   ^;  94   !;   0   ?;  94   :)

% 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(greater_or_equal_type,type,
    greater_or_equal: $i > $i > $o ).

thf(safe_type,type,
    safe: $i > $i > $o ).

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

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

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ ( s @ A ) ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ~ ( safe @ A @ B )
      | ~ ( safe @ ( s @ ( s @ 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(41,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ ( s @ A ) ) ) @ ( c @ B ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ~ ( safe @ A @ B )
      | ~ ( safe @ ( s @ ( s @ C ) ) @ D )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ ( s @ C ) ) ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ D ) ) ) )
      | ~ ( safe @ A @ ( s @ B ) )
      | ~ ( safe @ C @ 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(44,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ D ) ) ) )
      | ~ ( safe @ A @ ( s @ B ) )
      | ~ ( safe @ C @ D )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ~ ( safe @ A @ B )
      | ~ ( safe @ C @ ( s @ 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(39,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ~ ( safe @ A @ B )
      | ~ ( safe @ C @ ( s @ D ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ C ) @ ( c @ ( s @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ~ ( safe @ A @ B )
      | ~ ( safe @ ( s @ C ) @ ( s @ 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(35,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) )
      | ~ ( safe @ A @ B )
      | ~ ( safe @ ( s @ C ) @ ( s @ D ) )
      | ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ ( s @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(15,axiom,
    ! [A: $i] : ( greater_or_equal @ A @ n0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',great_eq_base) ).

thf(43,plain,
    ! [A: $i] : ( greater_or_equal @ A @ n0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

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

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ ( s @ D ) ) ) )
      | ~ ( safe @ ( s @ A ) @ ( s @ B ) )
      | ~ ( safe @ C @ 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(37,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( achievable @ ( west @ ( m @ A ) @ ( c @ B ) ) @ boatoneast @ ( east @ ( m @ ( s @ C ) ) @ ( c @ ( s @ D ) ) ) )
      | ~ ( safe @ ( s @ A ) @ ( s @ B ) )
      | ~ ( safe @ C @ D )
      | ( achievable @ ( west @ ( m @ ( s @ A ) ) @ ( c @ ( s @ B ) ) ) @ boatonwest @ ( east @ ( m @ C ) @ ( c @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

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

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

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( greater_or_equal @ ( s @ A ) @ ( s @ B ) )
      | ~ ( greater_or_equal @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',great_eq_recursive) ).

thf(33,plain,
    ! [B: $i,A: $i] :
      ( ( greater_or_equal @ ( s @ A ) @ ( s @ B ) )
      | ~ ( greater_or_equal @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(9,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(32,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)],[9]) ).

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

thf(4,axiom,
    ! [A: $i] : ( safe @ n0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_missionaries_is_safe) ).

thf(23,plain,
    ! [A: $i] : ( safe @ n0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( greater_or_equal @ A @ B )
      | ( safe @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',same_or_more_missionaries_is_safe) ).

thf(19,plain,
    ! [B: $i,A: $i] :
      ( ~ ( greater_or_equal @ A @ B )
      | ( safe @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(46,plain,
    $false,
    inference(e,[status(thm)],[41,44,39,35,43,24,37,28,21,33,32,17,26,23,30,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PUZ008-3 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n015.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 20:14:23 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.96/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.09/1.03  % [INFO] 	 Parsing done (137ms). 
% 1.38/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.76/1.28  % [INFO] 	 cvc4 registered as external prover. 
% 1.76/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.35  % [INFO] 	 Found a conjecture and 15 axioms. Running axiom selection ... 
% 2.02/1.40  % [INFO] 	 Axiom selection finished. Selected 15 axioms (removed 0 axioms). 
% 2.02/1.43  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.02/1.43  % [INFO] 	 Type checking passed. 
% 2.02/1.44  % [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 ... 
% 3.31/1.90  % External prover 'e' found a proof!
% 3.31/1.90  % [INFO] 	 Killing All external provers ... 
% 3.31/1.90  % Time passed: 1353ms (effective reasoning time: 862ms)
% 3.31/1.90  % 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)>
% 3.31/1.91  % Axioms used in derivation (15): no_missionaries_is_safe, cannibal_west_to_east, two_cannibals_west_to_east, cannibal_east_to_west, missionary_and_cannibal_east_to_west, missionary_east_to_west, missionary_west_to_east, two_cannibals_east_to_west, two_missionaries_east_to_west, great_eq_recursive, same_or_more_missionaries_is_safe, start_on_west_bank, missionary_and_cannibal_west_to_east, two_missionaries_west_to_east, great_eq_base
% 3.31/1.91  % No. of inferences in proof: 33
% 3.31/1.91  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1353 ms resp. 862 ms w/o parsing
% 3.80/1.99  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.80/1.99  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------