TSTP Solution File: SET865-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET865-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 : Fri May 19 11:54:43 EDT 2023

% Result   : Unsatisfiable 2.61s 1.54s
% Output   : Refutation 2.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   27 (   5 unt;  10 typ;   0 def)
%            Number of atoms       :   35 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  206 (  20   ~;  18   |;   0   &; 168   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   3 con; 0-3 aty)
%            Number of variables   :   32 (   0   ^;  32   !;   0   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_in_type,type,
    c_in: $i > $i > $i > $o ).

thf(c_Union_type,type,
    c_Union: $i > $i > $i ).

thf(t_a_type,type,
    t_a: $i ).

thf(v_S_type,type,
    v_S: $i ).

thf(tc_set_type,type,
    tc_set: $i > $i ).

thf(c_Zorn_Ochain_type,type,
    c_Zorn_Ochain: $i > $i > $i ).

thf(v_x_type,type,
    v_x: $i > $i ).

thf(c_lessequals_type,type,
    c_lessequals: $i > $i > $i > $o ).

thf(c_Zorn_OHausdorff__1_type,type,
    c_Zorn_OHausdorff__1: $i > $i > $i ).

thf(c_Zorn_Omaxchain_type,type,
    c_Zorn_Omaxchain: $i > $i > $i ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ( c_in @ ( v_x @ A ) @ v_S @ ( tc_set @ t_a ) )
      | ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(10,plain,
    ! [A: $i] :
      ( ( c_in @ ( v_x @ A ) @ v_S @ ( tc_set @ t_a ) )
      | ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Zorn_Omaxchain @ A @ B ) @ ( c_Zorn_Ochain @ A @ B ) @ ( tc_set @ ( tc_set @ ( tc_set @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).

thf(24,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Zorn_Omaxchain @ A @ B ) @ ( c_Zorn_Ochain @ A @ B ) @ ( tc_set @ ( tc_set @ ( tc_set @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Zorn_OHausdorff__1 @ A @ B ) @ ( c_Zorn_Omaxchain @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).

thf(20,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Zorn_OHausdorff__1 @ A @ B ) @ ( c_Zorn_Omaxchain @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_in @ D @ ( c_Zorn_Omaxchain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_lessequals @ ( c_Union @ D @ C ) @ A @ ( tc_set @ C ) )
      | ( ( c_Union @ D @ C )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).

thf(21,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_in @ D @ ( c_Zorn_Omaxchain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_lessequals @ ( c_Union @ D @ C ) @ A @ ( tc_set @ C ) )
      | ( ( c_Union @ D @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ( c_in @ ( c_Union @ A @ t_a ) @ v_S @ ( tc_set @ t_a ) )
      | ~ ( c_in @ A @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(9,plain,
    ! [A: $i] :
      ( ( c_in @ ( c_Union @ A @ t_a ) @ v_S @ ( tc_set @ t_a ) )
      | ~ ( c_in @ A @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(4,negated_conjecture,
    ! [A: $i] :
      ( ( A
       != ( v_x @ A ) )
      | ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(12,plain,
    ! [A: $i] :
      ( ( A
       != ( v_x @ A ) )
      | ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(18,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ( c_lessequals @ A @ ( v_x @ A ) @ ( tc_set @ t_a ) )
      | ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(11,plain,
    ! [A: $i] :
      ( ( c_lessequals @ A @ ( v_x @ A ) @ ( tc_set @ t_a ) )
      | ~ ( c_in @ A @ v_S @ ( tc_set @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(25,plain,
    $false,
    inference(cvc4,[status(thm)],[10,24,20,21,9,12,18,11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET865-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May 18 18:48:04 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.91/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.22/0.94  % [INFO] 	 Parsing done (110ms). 
% 1.22/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.14  % [INFO] 	 eprover registered as external prover. 
% 1.59/1.14  % [INFO] 	 cvc4 registered as external prover. 
% 1.59/1.14  % [INFO] 	 Scanning for conjecture ... 
% 1.68/1.20  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.68/1.23  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.85/1.23  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.85/1.24  % [INFO] 	 Type checking passed. 
% 1.85/1.24  % [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 ... 
% 2.61/1.54  % External prover 'cvc4' found a proof!
% 2.61/1.54  % [INFO] 	 Killing All external provers ... 
% 2.61/1.54  % Time passed: 1034ms (effective reasoning time: 591ms)
% 2.61/1.54  % 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)>
% 2.61/1.54  % Axioms used in derivation (4): cls_Zorn_Omaxchain__subset__chain_0, cls_Zorn_OHausdorff_0, cls_Zorn_Omaxchain__Zorn_0, cls_Set_OsubsetD_0
% 2.61/1.54  % No. of inferences in proof: 17
% 2.61/1.54  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1034 ms resp. 591 ms w/o parsing
% 2.77/1.58  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.77/1.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------