TSTP Solution File: SET847-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET847-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.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 11:54:36 EDT 2023

% Result   : Unsatisfiable 2.86s 1.64s
% Output   : Refutation 2.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   36 (   9 unt;  13 typ;   0 def)
%            Number of atoms       :   41 (   6 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  286 (  20   ~;  18   |;   0   &; 248   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   56 (   0   ^;  56   !;   0   ?;  56   :)

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

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

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

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

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

thf(c_minus_type,type,
    c_minus: $i > $i > $i > $i ).

thf(c_emptyset_type,type,
    c_emptyset: $i ).

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

thf(c_Main_OsubsetI__1_type,type,
    c_Main_OsubsetI__1: $i > $i > $i > $i ).

thf(c_Zorn_OTFin_type,type,
    c_Zorn_OTFin: $i > $i > $i ).

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

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

thf(c_Zorn_Osucc_type,type,
    c_Zorn_Osucc: $i > $i > $i > $i ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).

thf(14,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) )
      | ( ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) )
        = ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oequal__succ__Union_1) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) )
      | ( ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) )
        = ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(21,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_minus @ ( c_Zorn_Ochain @ B @ C ) @ ( c_Zorn_Omaxchain @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( ( c_Zorn_Osucc @ B @ A @ C )
       != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).

thf(32,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_minus @ ( c_Zorn_Ochain @ B @ C ) @ ( c_Zorn_Omaxchain @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( ( c_Zorn_Osucc @ B @ A @ C )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_in @ A @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__chain__lemma4_0) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_in @ A @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

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

thf(12,plain,
    ! [A: $i] :
      ~ ( c_in @ A @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(4,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).

thf(18,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(19,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(7,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).

thf(24,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) )
      | ( c_in @ ( c_Union @ A @ ( tc_set @ C ) ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) )
      | ( c_in @ ( c_Union @ A @ ( tc_set @ C ) ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(35,plain,
    $false,
    inference(e,[status(thm)],[14,29,21,32,27,12,18,16,19,24,25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET847-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n029.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu May 18 19:06:44 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.87/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.96  % [INFO] 	 Parsing done (118ms). 
% 1.19/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.51/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.24  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 1.87/1.26  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 1.87/1.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.87/1.28  % [INFO] 	 Type checking passed. 
% 1.87/1.29  % [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 ... 
% 2.86/1.63  % External prover 'e' found a proof!
% 2.86/1.63  % [INFO] 	 Killing All external provers ... 
% 2.86/1.64  % Time passed: 1119ms (effective reasoning time: 663ms)
% 2.86/1.64  % 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)>
% 2.86/1.64  % Axioms used in derivation (10): cls_Set_OemptyE_0, cls_Set_Osubset__refl_0, cls_Set_OsubsetI_0, cls_Zorn_Osucc__not__equals_0, cls_Set_Oempty__subsetI_0, cls_Set_Osubset__antisym_0, cls_Zorn_Oequal__succ__Union_1, cls_Set_ODiffI_0, cls_Zorn_OTFin__UnionI_0, cls_Zorn_OTFin__chain__lemma4_0
% 2.86/1.64  % No. of inferences in proof: 23
% 2.86/1.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1119 ms resp. 663 ms w/o parsing
% 2.86/1.69  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.86/1.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------