TSTP Solution File: SET025-8 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET025-8 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 03:04:57 EDT 2024

% Result   : Unsatisfiable 127.37s 23.75s
% Output   : Refutation 127.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   24 (  12 unt;   6 typ;   0 def)
%            Number of atoms       :   27 (   9 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   69 (  16   ~;   7   |;   0   &;  46   @)
%                                         (   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     :    9 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   16 (   0   ^  16   !;   0   ?;  16   :)

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

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

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

thf(ordered_pair_predicate_type,type,
    ordered_pair_predicate: $i > $o ).

thf(f2_type,type,
    f2: $i > $i ).

thf(f3_type,type,
    f3: $i > $i ).

thf(77,axiom,
    ! [A: $i] :
      ( ~ ( ordered_pair_predicate @ A )
      | ( A
        = ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate3) ).

thf(324,plain,
    ! [A: $i] :
      ( ~ ( ordered_pair_predicate @ A )
      | ( A
        = ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(325,plain,
    ! [A: $i] :
      ( ~ ( ordered_pair_predicate @ A )
      | ( A
        = ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) ) ) ),
    inference(cnf,[status(esa)],[324]) ).

thf(326,plain,
    ! [A: $i] :
      ( ( ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) )
        = A )
      | ~ ( ordered_pair_predicate @ A ) ),
    inference(lifteq,[status(thm)],[325]) ).

thf(108,axiom,
    ! [B: $i,A: $i] : ( little_set @ ( ordered_pair @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pairs_are_small1) ).

thf(398,plain,
    ! [B: $i,A: $i] : ( little_set @ ( ordered_pair @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(1,negated_conjecture,
    ~ ( little_set @ a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_predicate_is_small) ).

thf(150,plain,
    ~ ( little_set @ a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(151,plain,
    ~ ( little_set @ a ),
    inference(polarity_switch,[status(thm)],[150]) ).

thf(507,plain,
    ! [B: $i,A: $i] :
      ( ( little_set @ ( ordered_pair @ A @ B ) )
     != ( little_set @ a ) ),
    inference(paramod_ordered,[status(thm)],[398,151]) ).

thf(508,plain,
    ! [B: $i,A: $i] :
      ( ( ordered_pair @ A @ B )
     != a ),
    inference(simp,[status(thm)],[507]) ).

thf(72509,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ordered_pair_predicate @ A )
      | ( A != a )
      | ( ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) )
       != ( ordered_pair @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[326,508]) ).

thf(72510,plain,
    ! [A: $i] :
      ( ~ ( ordered_pair_predicate @ A )
      | ( A != a ) ),
    inference(pattern_uni,[status(thm)],[72509:[bind(A,$thf( E )),bind(B,$thf( f2 @ E )),bind(C,$thf( f3 @ E ))]]) ).

thf(72644,plain,
    ~ ( ordered_pair_predicate @ a ),
    inference(simp,[status(thm)],[72510]) ).

thf(129,axiom,
    ordered_pair_predicate @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).

thf(457,plain,
    ordered_pair_predicate @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(72673,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[72644,457]) ).

thf(72674,plain,
    $false,
    inference(simp,[status(thm)],[72673]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET025-8 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n006.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 13:18:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.83/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.47/1.01  % [INFO] 	 Parsing done (156ms). 
% 1.47/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.89/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.89/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 152 axioms. Running axiom selection ... 
% 2.27/1.35  % [INFO] 	 Axiom selection finished. Selected 148 axioms (removed 4 axioms). 
% 2.54/1.44  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.54/1.45  % [INFO] 	 Type checking passed. 
% 2.54/1.45  % [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 ... 
% 127.37/23.75  % [INFO] 	 Killing All external provers ... 
% 127.37/23.75  % Time passed: 23221ms (effective reasoning time: 22725ms)
% 127.37/23.75  % Axioms used in derivation (3): ordered_pair_predicate3, ordered_pairs_are_small1, an_ordered_pair_predicate
% 127.37/23.75  % No. of inferences in proof: 18
% 127.37/23.75  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 23221 ms resp. 22725 ms w/o parsing
% 127.37/23.77  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 127.37/23.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------