TSTP Solution File: PRO029^16 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : PRO029^16 : TPTP v8.1.2. Released v8.1.0.
% 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  7 08:03:26 EDT 2024

% Result   : Theorem 3.09s 1.90s
% Output   : Refutation 3.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   43 (  10 unt;  14 typ;   5 def)
%            Number of atoms       :  136 (   5 equ;   0 cnn)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  245 (  11   ~;   0   |;   8   &; 198   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   32 (  32   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :   42 (  12   ^  30   !;   0   ?;  42   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mworld_type,type,
    mworld: $tType ).

thf(mindex_type,type,
    mindex: $tType ).

thf(mrel_type,type,
    mrel: mindex > mworld > mworld > $o ).

thf('\'#c\'_type',type,
    '\'#c\'': mindex ).

thf('\'#u\'_type',type,
    '\'#u\'': mindex ).

thf(mactual_type,type,
    mactual: mworld ).

thf(mlocal_type,type,
    mlocal: ( mworld > $o ) > $o ).

thf(mlocal_def,definition,
    ( mlocal
    = ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).

thf(mnot_type,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: mworld > $o,B: mworld] :
          ~ ( A @ B ) ) ) ).

thf(mand_type,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
          & ( B @ C ) ) ) ) ).

thf(mimplies_type,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
         => ( B @ C ) ) ) ) ).

thf(mbox_type,type,
    mbox: mindex > ( mworld > $o ) > mworld > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: mindex,B: mworld > $o,C: mworld] :
        ! [D: mworld] :
          ( ( mrel @ A @ C @ D )
         => ( B @ D ) ) ) ) ).

thf(charge_type,type,
    charge: mworld > $o ).

thf(called_type,type,
    called: mworld > $o ).

thf(paid_type,type,
    paid: mworld > $o ).

thf(8,axiom,
    mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '\'#u\'' @ charge ) @ ( mbox @ '\'#c\'' @ charge ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_charge_u) ).

thf(29,plain,
    ( ( charge @ mactual )
   => ( ! [A: mworld] :
          ( ( mrel @ '\'#u\'' @ mactual @ A )
         => ( charge @ A ) )
      & ! [A: mworld] :
          ( ( mrel @ '\'#c\'' @ mactual @ A )
         => ( charge @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1,conjecture,
    mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '\'#u\'' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',requirement_1) ).

thf(2,negated_conjecture,
    ~ ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '\'#u\'' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(13,plain,
    ~ ( ~ ( ( charge @ mactual )
         => ( ( called @ mactual )
            & ~ ( paid @ mactual ) ) )
     => ! [A: mworld] :
          ( ( mrel @ '\'#u\'' @ mactual @ A )
         => ~ ( ( charge @ A )
             => ( ( called @ A )
                & ~ ( paid @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    mlocal @ ( mimplies @ paid @ called ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aciom_paid_charge) ).

thf(27,plain,
    ( ( paid @ mactual )
   => ( called @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(10,axiom,
    mlocal @ ( mbox @ '\'#c\'' @ ( mimplies @ paid @ ( mbox @ '\'#u\'' @ paid ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

thf(35,plain,
    ! [A: mworld] :
      ( ( mrel @ '\'#c\'' @ mactual @ A )
     => ( ( paid @ A )
       => ! [B: mworld] :
            ( ( mrel @ '\'#u\'' @ A @ B )
           => ( paid @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(3,axiom,
    ! [A: mworld] : ( mrel @ '\'#c\'' @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#c_reflexive') ).

thf(19,plain,
    ! [A: mworld] : ( mrel @ '\'#c\'' @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,axiom,
    mlocal @ ( mimplies @ ( mnot @ ( mbox @ '\'#c\'' @ called ) ) @ ( mbox @ '\'#u\'' @ ( mnot @ ( mbox @ '\'#c\'' @ called ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(37,plain,
    ( ~ ! [A: mworld] :
          ( ( mrel @ '\'#c\'' @ mactual @ A )
         => ( called @ A ) )
   => ! [A: mworld] :
        ( ( mrel @ '\'#u\'' @ mactual @ A )
       => ~ ! [B: mworld] :
              ( ( mrel @ '\'#c\'' @ A @ B )
             => ( called @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(6,axiom,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ '\'#u\'' @ A @ B )
        & ( mrel @ '\'#u\'' @ B @ C ) )
     => ( mrel @ '\'#u\'' @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#u_transitive') ).

thf(25,plain,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ '\'#u\'' @ A @ B )
        & ( mrel @ '\'#u\'' @ B @ C ) )
     => ( mrel @ '\'#u\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ '\'#c\'' @ A @ B )
        & ( mrel @ '\'#c\'' @ B @ C ) )
     => ( mrel @ '\'#c\'' @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#c_transitive') ).

thf(21,plain,
    ! [A: mworld,B: mworld,C: mworld] :
      ( ( ( mrel @ '\'#c\'' @ A @ B )
        & ( mrel @ '\'#c\'' @ B @ C ) )
     => ( mrel @ '\'#c\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
    mlocal @ ( mbox @ '\'#u\'' @ ( mimplies @ called @ ( mbox @ '\'#c\'' @ called ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

thf(33,plain,
    ! [A: mworld] :
      ( ( mrel @ '\'#u\'' @ mactual @ A )
     => ( ( called @ A )
       => ! [B: mworld] :
            ( ( mrel @ '\'#c\'' @ A @ B )
           => ( called @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(12,axiom,
    mlocal @ ( mimplies @ ( mnot @ ( mbox @ '\'#u\'' @ paid ) ) @ ( mbox @ '\'#c\'' @ ( mnot @ ( mbox @ '\'#u\'' @ paid ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

thf(40,plain,
    ( ~ ! [A: mworld] :
          ( ( mrel @ '\'#u\'' @ mactual @ A )
         => ( paid @ A ) )
   => ! [A: mworld] :
        ( ( mrel @ '\'#c\'' @ mactual @ A )
       => ~ ! [B: mworld] :
              ( ( mrel @ '\'#u\'' @ A @ B )
             => ( paid @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(5,axiom,
    ! [A: mworld] : ( mrel @ '\'#u\'' @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#u_reflexive') ).

thf(23,plain,
    ! [A: mworld] : ( mrel @ '\'#u\'' @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(43,plain,
    $false,
    inference(e,[status(thm)],[29,13,27,35,19,37,25,21,33,40,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : PRO029^16 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n027.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 : Mon May  6 15:56:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.02/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.13  % [INFO] 	 Parsing done (136ms). 
% 1.28/1.14  % [INFO] 	 Running in sequential loop mode. 
% 1.86/1.38  % [INFO] 	 eprover registered as external prover. 
% 1.86/1.38  % [INFO] 	 cvc4 registered as external prover. 
% 1.86/1.38  % [INFO] 	 Scanning for conjecture ... 
% 2.14/1.46  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 2.16/1.48  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 2.16/1.49  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.16/1.50  % [INFO] 	 Type checking passed. 
% 2.16/1.50  % [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 ... 
% 3.09/1.89  % External prover 'e' found a proof!
% 3.09/1.89  % [INFO] 	 Killing All external provers ... 
% 3.09/1.89  % Time passed: 1262ms (effective reasoning time: 752ms)
% 3.09/1.89  % 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)>
% 3.09/1.90  % Axioms used in derivation (10): mrel_#c_reflexive, axiom_2, mrel_#u_reflexive, axiom_charge_u, axiom_3, axiom_1, aciom_paid_charge, mrel_#u_transitive, mrel_#c_transitive, axiom_4
% 3.09/1.90  % No. of inferences in proof: 24
% 3.09/1.90  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1262 ms resp. 752 ms w/o parsing
% 3.63/2.00  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.63/2.00  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------