TSTP Solution File: SYO160^5 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO160^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 08:59:27 EDT 2024

% Result   : Theorem 3.16s 1.77s
% Output   : Refutation 3.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (   2 unt;   6 typ;   0 def)
%            Number of atoms       :   64 (   3 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  113 (  16   ~;  20   |;  12   &;  56   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   31 (   0   ^  31   !;   0   ?;  31   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_type,type,
    c: $i ).

thf(cR_type,type,
    cR: $i > $o ).

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

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

thf(cQ_type,type,
    cQ: $i > $o ).

thf(cP_type,type,
    cP: $i > $o ).

thf(1,conjecture,
    ( ( ( ! [A: $i] : ( cP @ A )
        | ! [A: $i] : ( cQ @ A ) )
      & ! [A: $i] :
          ( ( cP @ A )
         => ( cR @ A ) )
      & ! [A: $i] :
          ( ( cQ @ A )
         => ( cR @ A ) ) )
   => ( ( cR @ a )
      & ( cR @ b )
      & ( cR @ c ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDISJ_THIRD) ).

thf(2,negated_conjecture,
    ~ ( ( ( ! [A: $i] : ( cP @ A )
          | ! [A: $i] : ( cQ @ A ) )
        & ! [A: $i] :
            ( ( cP @ A )
           => ( cR @ A ) )
        & ! [A: $i] :
            ( ( cQ @ A )
           => ( cR @ A ) ) )
     => ( ( cR @ a )
        & ( cR @ b )
        & ( cR @ c ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ( ! [A: $i] : ( cP @ A )
          | ! [A: $i] : ( cQ @ A ) )
        & ! [A: $i] :
            ( ( cP @ A )
           => ( cR @ A ) )
        & ! [A: $i] :
            ( ( cQ @ A )
           => ( cR @ A ) ) )
     => ( ( cR @ a )
        & ( cR @ b )
        & ( cR @ c ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ~ ( cR @ a )
    | ~ ( cR @ b )
    | ~ ( cR @ c ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A )
      | ( cQ @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [A: $i] :
      ( ~ ( cQ @ A )
      | ( cR @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( cQ @ A )
      | ( cR @ A ) ),
    inference(simp,[status(thm)],[5]) ).

thf(10,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cP @ A )
      | ( cR @ C )
      | ( ( cQ @ B )
       != ( cQ @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[7,8]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ A )
      | ( cR @ B ) ),
    inference(pattern_uni,[status(thm)],[10:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(6,plain,
    ! [A: $i] :
      ( ~ ( cP @ A )
      | ( cR @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: $i] :
      ( ~ ( cP @ A )
      | ( cR @ A ) ),
    inference(simp,[status(thm)],[6]) ).

thf(14,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cR @ B )
      | ( cR @ C )
      | ( ( cP @ A )
       != ( cP @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[11,9]) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( cR @ B )
      | ( cR @ A ) ),
    inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).

thf(57,plain,
    ! [B: $i,A: $i] :
      ( ( cR @ B )
      | ( ( cR @ A )
       != ( cR @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[15]) ).

thf(58,plain,
    ! [A: $i] : ( cR @ A ),
    inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(64,plain,
    ( ~ $true
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[4,58]) ).

thf(65,plain,
    $false,
    inference(simp,[status(thm)],[64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO160^5 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May 20 09:12:09 EDT 2024
% 0.22/0.36  % CPUTime  : 
% 0.92/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/0.97  % [INFO] 	 Parsing done (106ms). 
% 1.21/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.20  % [INFO] 	 nitpick registered as external prover. 
% 1.60/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.72/1.28  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.72/1.28  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.72/1.29  % [INFO] 	 Type checking passed. 
% 1.72/1.29  % [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 ... 
% 3.16/1.77  % [INFO] 	 Killing All external provers ... 
% 3.16/1.77  % Time passed: 1250ms (effective reasoning time: 791ms)
% 3.16/1.77  % 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)>
% 3.16/1.77  % Axioms used in derivation (0): 
% 3.16/1.77  % No. of inferences in proof: 17
% 3.16/1.77  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1250 ms resp. 791 ms w/o parsing
% 3.16/1.80  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.16/1.80  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------