TSTP Solution File: SET025-3 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET025-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Tue May 21 03:04:56 EDT 2024

% Result   : Unsatisfiable 7.16s 2.49s
% Output   : Refutation 7.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   20 (  13 unt;   6 typ;   0 def)
%            Number of atoms       :   17 (   9 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   75 (   9   ~;   1   |;   0   &;  65   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   22 (   0   ^  22   !;   0   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
thf(little_set_type,type,
    little_set: $i > $o ).

thf(ordered_pair_type,type,
    ordered_pair: $i > $i > $i ).

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

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

thf(singleton_set_type,type,
    singleton_set: $i > $i ).

thf(non_ordered_pair_type,type,
    non_ordered_pair: $i > $i > $i ).

thf(115,axiom,
    ! [B: $i,A: $i] :
      ( ( ordered_pair @ A @ B )
      = ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).

thf(418,plain,
    ! [B: $i,A: $i] :
      ( ( ordered_pair @ A @ B )
      = ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(419,plain,
    ! [B: $i,A: $i] :
      ( ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) )
      = ( ordered_pair @ A @ B ) ),
    inference(lifteq,[status(thm)],[418]) ).

thf(139,axiom,
    ! [B: $i,A: $i] : ( little_set @ ( non_ordered_pair @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair4) ).

thf(476,plain,
    ! [B: $i,A: $i] : ( little_set @ ( non_ordered_pair @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(1,negated_conjecture,
    ~ ( little_set @ ( ordered_pair @ a @ b ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pairs_are_small) ).

thf(148,plain,
    ~ ( little_set @ ( ordered_pair @ a @ b ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(149,plain,
    ~ ( little_set @ ( ordered_pair @ a @ b ) ),
    inference(polarity_switch,[status(thm)],[148]) ).

thf(503,plain,
    ! [B: $i,A: $i] :
      ( ( little_set @ ( non_ordered_pair @ A @ B ) )
     != ( little_set @ ( ordered_pair @ a @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[476,149]) ).

thf(504,plain,
    ! [B: $i,A: $i] :
      ( ( non_ordered_pair @ A @ B )
     != ( ordered_pair @ a @ b ) ),
    inference(simp,[status(thm)],[503]) ).

thf(628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ordered_pair @ A @ B )
       != ( ordered_pair @ a @ b ) )
      | ( ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) )
       != ( non_ordered_pair @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[419,504]) ).

thf(629,plain,
    ! [B: $i,A: $i] :
      ( ( ordered_pair @ A @ B )
     != ( ordered_pair @ a @ b ) ),
    inference(pattern_uni,[status(thm)],[628:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( singleton_set @ F )),bind(D,$thf( non_ordered_pair @ F @ G ))]]) ).

thf(638,plain,
    ! [B: $i,A: $i] :
      ( ( ordered_pair @ A @ B )
     != ( ordered_pair @ a @ b ) ),
    inference(simp,[status(thm)],[629]) ).

thf(642,plain,
    $false,
    inference(pattern_uni,[status(thm)],[638:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET025-3 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.13  % Command  : run_Leo-III %s %d
% 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 : Mon May 20 12:20:09 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.95/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.22/1.01  % [INFO] 	 Parsing done (157ms). 
% 1.53/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.88/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.88/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 150 axioms. Running axiom selection ... 
% 2.15/1.35  % [INFO] 	 Axiom selection finished. Selected 146 axioms (removed 4 axioms). 
% 2.43/1.43  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.43/1.44  % [INFO] 	 Type checking passed. 
% 2.43/1.45  % [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 ... 
% 7.16/2.48  % [INFO] 	 Killing All external provers ... 
% 7.16/2.49  % Time passed: 1968ms (effective reasoning time: 1462ms)
% 7.16/2.49  % Axioms used in derivation (2): ordered_pair, non_ordered_pair4
% 7.16/2.49  % No. of inferences in proof: 14
% 7.16/2.49  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1968 ms resp. 1462 ms w/o parsing
% 7.16/2.50  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.16/2.50  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------