%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : QUA004^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n020.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 : Mon Jun 24 13:52:27 EDT 2024

% Result   : Theorem 3.08s 1.65s
% Output   : Refutation 3.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   12 (  12 unt;   0 typ;   2 def)
%            Number of atoms       :   24 (  18 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :   21 (   4   ~;   0   |;   0   &;  17   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   17 (  10   ^   7   !;   0   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
thf(singleton_type,type,
    singleton: $i > $i > $o ).

thf(singleton_def,definition,
    ( singleton
    = ( ^ [A: $i,B: $i] : ( B = A ) ) ) ).

thf(sup_type,type,
    sup: ( $i > $o ) > $i ).

thf(addition_type,type,
    addition: $i > $i > $i ).

thf(addition_def,definition,
    ( addition
    = ( ^ [A: $i,B: $i] : ( sup @ ( union @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( addition @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_idemp) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( addition @ A @ A )
        = A ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: $i] :
        ( ( sup
          @ ^ [B: $i] : ( B = A ) )
        = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,plain,
    ( ( sup
      @ ^ [A: $i] : ( A = sk1 ) )
   != sk1 ),
    inference(cnf,[status(esa)],[10]) ).

thf(12,plain,
    ( ( sup
      @ ^ [A: $i] : ( A = sk1 ) )
   != sk1 ),
    inference(lifteq,[status(thm)],[11]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( sup @ ( singleton @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sup_singleset) ).

thf(15,plain,
    ! [A: $i] :
      ( ( sup
        @ ^ [B: $i] : ( B = A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(16,plain,
    ! [A: $i] :
      ( ( sup
        @ ^ [B: $i] : ( B = A ) )
      = A ),
    inference(cnf,[status(esa)],[15]) ).

thf(17,plain,
    ! [A: $i] :
      ( ( sup
        @ ^ [B: $i] : ( B = A ) )
      = A ),
    inference(lifteq,[status(thm)],[16]) ).

thf(35,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[12,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : QUA004^1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.13  % Command  : run_Leo-III %s %d SAT
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Jun 23 18:14:26 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.97  % [INFO] 	 Parsing done (107ms). 
% 1.20/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 1.92/1.26  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.99/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.99/1.27  % [INFO] 	 Type checking passed. 
% 1.99/1.28  % [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 ... 
% 2.77/1.64  % [INFO] 	 Killing All external provers ... 
% 2.77/1.65  % Time passed: 1110ms (effective reasoning time: 663ms)
% 2.77/1.65  % 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)>
% 3.08/1.65  % Axioms used in derivation (1): sup_singleset
% 3.08/1.65  % No. of inferences in proof: 10
% 3.08/1.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1110 ms resp. 663 ms w/o parsing
% 3.08/1.66  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.08/1.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------