TSTP Solution File: SET820-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET820-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 11:54:25 EDT 2023

% Result   : Unsatisfiable 3.00s 1.69s
% Output   : Refutation 3.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   20 (   7 unt;   7 typ;   0 def)
%            Number of atoms       :   21 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   80 (  10   ~;   8   |;   0   &;  62   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   26 (   0   ^;  26   !;   0   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v_P_type,type,
    v_P: $i > $o ).

thf(v_a_type,type,
    v_a: $i ).

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

thf(tc_IntDef_Oint_type,type,
    tc_IntDef_Oint: $i ).

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

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

thf(c_insert_type,type,
    c_insert: $i > $i > $i > $i ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).

thf(14,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_IntDef_Oint )
      | ~ ( v_P @ ( v_x @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_IntDef_Oint )
      | ~ ( v_P @ ( v_x @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,negated_conjecture,
    v_P @ v_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(7,plain,
    v_P @ v_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_IntDef_Oint )
      | ( c_in @ ( v_x @ B ) @ B @ tc_IntDef_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(15,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(21,plain,
    $false,
    inference(e,[status(thm)],[14,9,12,7,8,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET820-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n017.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 18:16:01 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.92/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.00  % [INFO] 	 Parsing done (116ms). 
% 1.25/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.57/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.57/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.27  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.87/1.29  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.87/1.30  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.87/1.30  % [INFO] 	 Type checking passed. 
% 1.87/1.30  % [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 ... 
% 2.88/1.69  % External prover 'e' found a proof!
% 2.88/1.69  % [INFO] 	 Killing All external provers ... 
% 2.88/1.69  % Time passed: 1163ms (effective reasoning time: 679ms)
% 2.88/1.69  % 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)>
% 3.00/1.69  % Axioms used in derivation (3): cls_Set_OinsertCI_1, cls_Set_OemptyE_0, cls_Set_OinsertE_0
% 3.00/1.69  % No. of inferences in proof: 13
% 3.00/1.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1163 ms resp. 679 ms w/o parsing
% 3.00/1.73  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.00/1.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------