TSTP Solution File: SET930+1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET930+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 03:04:34 EDT 2024

% Result   : Theorem 3.21s 1.69s
% Output   : Refutation 3.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   26 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :   55 (  26 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  228 (  30   ~;   3   |;  21   &; 163   @)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   0   ^  35   !;   4   ?;  39   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_difference_type,type,
    set_difference: $i > $i > $i ).

thf(unordered_pair_type,type,
    unordered_pair: $i > $i > $i ).

thf(empty_set_type,type,
    empty_set: $i ).

thf(singleton_type,type,
    singleton: $i > $i ).

thf(in_type,type,
    in: $i > $i > $o ).

thf(empty_type,type,
    empty: $i > $o ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(21,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
        = empty_set )
    <=> ( ( in @ A @ C )
        & ( in @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).

thf(53,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
          = empty_set )
       => ( ( in @ A @ C )
          & ( in @ B @ C ) ) )
      & ( ( ( in @ A @ C )
          & ( in @ B @ C ) )
       => ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
          = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(8,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(41,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(7,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(39,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
         != empty_set )
        & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
         != ( singleton @ A ) )
        & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
         != ( singleton @ B ) )
        & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
         != ( unordered_pair @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ~ ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
           != empty_set )
          & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
           != ( singleton @ A ) )
          & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
           != ( singleton @ B ) )
          & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
           != ( unordered_pair @ A @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(11,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ~ ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
           != empty_set )
          & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
           != ( singleton @ A ) )
          & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
           != ( singleton @ B ) )
          & ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
           != ( unordered_pair @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
        = ( unordered_pair @ A @ B ) )
    <=> ( ~ ( in @ A @ C )
        & ~ ( in @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).

thf(44,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
          = ( unordered_pair @ A @ B ) )
       => ( ~ ( in @ A @ C )
          & ~ ( in @ B @ C ) ) )
      & ( ( ~ ( in @ A @ C )
          & ~ ( in @ B @ C ) )
       => ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
          = ( unordered_pair @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
        = ( singleton @ A ) )
    <=> ( ~ ( in @ A @ C )
        & ( ( in @ B @ C )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).

thf(27,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
          = ( singleton @ A ) )
       => ( ~ ( in @ A @ C )
          & ( ( in @ B @ C )
            | ( A = B ) ) ) )
      & ( ( ~ ( in @ A @ C )
          & ( ( in @ B @ C )
            | ( A = B ) ) )
       => ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
          = ( singleton @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    empty @ empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(26,plain,
    empty @ empty_set,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

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

thf(62,plain,
    $false,
    inference(e,[status(thm)],[21,53,41,39,11,44,27,26,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET930+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n007.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 20 11:25:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.95/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/0.99  % [INFO] 	 Parsing done (104ms). 
% 1.28/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.64/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.64/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.81/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 1.88/1.28  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.88/1.29  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.88/1.30  % [INFO] 	 Type checking passed. 
% 1.88/1.30  % [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 ... 
% 3.21/1.69  % External prover 'e' found a proof!
% 3.21/1.69  % [INFO] 	 Killing All external provers ... 
% 3.21/1.69  % Time passed: 1136ms (effective reasoning time: 682ms)
% 3.21/1.69  % 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)>
% 3.21/1.69  % Axioms used in derivation (8): fc1_xboole_0, t72_zfmisc_1, commutativity_k2_tarski, t73_zfmisc_1, rc1_xboole_0, l39_zfmisc_1, rc2_xboole_0, antisymmetry_r2_hidden
% 3.21/1.69  % No. of inferences in proof: 20
% 3.21/1.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1136 ms resp. 682 ms w/o parsing
% 3.21/1.73  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.21/1.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------