TSTP Solution File: SET108-6 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET108-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 03:05:25 EDT 2024

% Result   : Unsatisfiable 145.78s 26.04s
% Output   : Refutation 145.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   25 (  10 unt;   8 typ;   0 def)
%            Number of atoms       :   27 (  11 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  181 (  17   ~;   8   |;   0   &; 156   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   19 (   0   ^  19   !;   0   ?;  19   :)

% Comments : 
%------------------------------------------------------------------------------
thf(member_type,type,
    member: $i > $i > $o ).

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

thf(y_type,type,
    y: $i ).

thf(z_type,type,
    z: $i ).

thf(cross_product_type,type,
    cross_product: $i > $i > $i ).

thf(universal_class_type,type,
    universal_class: $i ).

thf(first_type,type,
    first: $i > $i ).

thf(second_type,type,
    second: $i > $i ).

thf(1,negated_conjecture,
    member @ ( ordered_pair @ y @ z ) @ ( cross_product @ universal_class @ universal_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_1) ).

thf(94,plain,
    member @ ( ordered_pair @ y @ z ) @ ( cross_product @ universal_class @ universal_class ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( cross_product @ B @ C ) )
      | ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).

thf(209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( cross_product @ B @ C ) )
      | ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(210,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( cross_product @ B @ C ) )
      | ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
        = A ) ),
    inference(cnf,[status(esa)],[209]) ).

thf(211,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
        = A )
      | ~ ( member @ A @ ( cross_product @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[210]) ).

thf(2,negated_conjecture,
    ~ ( member @ ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) @ ( cross_product @ universal_class @ universal_class ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_2) ).

thf(95,plain,
    ~ ( member @ ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) @ ( cross_product @ universal_class @ universal_class ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(96,plain,
    ~ ( member @ ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) @ ( cross_product @ universal_class @ universal_class ) ),
    inference(polarity_switch,[status(thm)],[95]) ).

thf(292,plain,
    ( ( member @ ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) @ ( cross_product @ universal_class @ universal_class ) )
   != ( member @ ( ordered_pair @ y @ z ) @ ( cross_product @ universal_class @ universal_class ) ) ),
    inference(paramod_ordered,[status(thm)],[94,96]) ).

thf(293,plain,
    ( ( ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) )
     != ( ordered_pair @ y @ z ) )
    | ( ( cross_product @ universal_class @ universal_class )
     != ( cross_product @ universal_class @ universal_class ) ) ),
    inference(simp,[status(thm)],[292]) ).

thf(294,plain,
    ( ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) )
   != ( ordered_pair @ y @ z ) ),
    inference(simp,[status(thm)],[293]) ).

thf(58523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( cross_product @ B @ C ) )
      | ( A
       != ( ordered_pair @ y @ z ) )
      | ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
       != ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[211,294]) ).

thf(58524,plain,
    ! [B: $i,A: $i] :
      ( ~ ( member @ ( ordered_pair @ y @ z ) @ ( cross_product @ A @ B ) )
      | ( ( ordered_pair @ y @ z )
       != ( ordered_pair @ y @ z ) ) ),
    inference(pattern_uni,[status(thm)],[58523:[bind(A,$thf( ordered_pair @ y @ z )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).

thf(58685,plain,
    ! [B: $i,A: $i] :
      ~ ( member @ ( ordered_pair @ y @ z ) @ ( cross_product @ A @ B ) ),
    inference(simp,[status(thm)],[58524]) ).

thf(58989,plain,
    $false,
    inference(rewrite,[status(thm)],[94,58685]) ).

thf(58990,plain,
    $false,
    inference(simp,[status(thm)],[58989]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET108-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n024.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 12:39:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.93/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.51/1.06  % [INFO] 	 Parsing done (156ms). 
% 1.51/1.07  % [INFO] 	 Running in sequential loop mode. 
% 2.00/1.27  % [INFO] 	 nitpick registered as external prover. 
% 2.00/1.27  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ... 
% 2.32/1.39  % [INFO] 	 Axiom selection finished. Selected 91 axioms (removed 0 axioms). 
% 2.64/1.46  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.64/1.47  % [INFO] 	 Type checking passed. 
% 2.64/1.47  % [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 ... 
% 145.78/26.04  % [INFO] 	 Killing All external provers ... 
% 145.78/26.04  % Time passed: 25506ms (effective reasoning time: 24968ms)
% 145.78/26.04  % Axioms used in derivation (1): cartesian_product4
% 145.78/26.04  % No. of inferences in proof: 17
% 145.78/26.04  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25506 ms resp. 24968 ms w/o parsing
% 145.78/26.06  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 145.78/26.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------