TSTP Solution File: SYO061^4 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO061^4 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 08:55:38 EDT 2024

% Result   : Theorem 2.72s 1.66s
% Output   : Refutation 2.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   19 (   6 unt;   6 typ;   3 def)
%            Number of atoms       :   45 (   3 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   62 (   4   ~;   2   |;   2   &;  48   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   17 (   3   ^  14   !;   0   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
thf(irel_type,type,
    irel: $i > $i > $o ).

thf(iatom_type,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(iatom_def,definition,
    ( iatom
    = ( ^ [A: $i > $o] : A ) ) ).

thf(iimplies_type,type,
    iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(iimplies_def,definition,
    ( iimplies
    = ( ^ [A: $i > $o,B: $i > $o] : ( mimplies @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).

thf(ivalid_type,type,
    ivalid: ( $i > $o ) > $o ).

thf(ivalid_def,definition,
    ( ivalid
    = ( '!' @ $i ) ) ).

thf(a_type,type,
    a: $i > $o ).

thf(b_type,type,
    b: $i > $o ).

thf(1,conjecture,
    ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: $i] :
        ( ~ ! [B: $i] :
              ( ( irel @ A @ B )
             => ( a @ B ) )
        | ! [B: $i] :
            ( ( irel @ A @ B )
           => ( b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i] : ( irel @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).

thf(10,plain,
    ! [A: $i] : ( irel @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( irel @ A @ B )
        & ( irel @ B @ C ) )
     => ( irel @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom) ).

thf(12,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( irel @ A @ B )
        & ( irel @ B @ C ) )
     => ( irel @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ ! [B: $i] :
            ( ( irel @ A @ B )
           => ( a @ B ) )
      | ! [B: $i] :
          ( ( irel @ A @ B )
         => ( b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(17,plain,
    $false,
    inference(e,[status(thm)],[6,10,12,14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYO061^4 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n023.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 10:31:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.35/1.00  % [INFO] 	 Parsing done (132ms). 
% 1.35/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.79/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.79/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.79/1.25  % [INFO] 	 Scanning for conjecture ... 
% 2.01/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.01/1.35  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.01/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.01/1.35  % [INFO] 	 Type checking passed. 
% 2.01/1.36  % [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 ... 
% 2.72/1.66  % External prover 'e' found a proof!
% 2.72/1.66  % [INFO] 	 Killing All external provers ... 
% 2.72/1.66  % Time passed: 1130ms (effective reasoning time: 642ms)
% 2.72/1.66  % 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)>
% 2.72/1.66  % Axioms used in derivation (3): refl_axiom, trans_axiom, axiom1
% 2.72/1.66  % No. of inferences in proof: 10
% 2.72/1.66  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1130 ms resp. 642 ms w/o parsing
% 2.72/1.69  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.72/1.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------