%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET855-2 : 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 11:54:40 EDT 2023

% Result   : Unsatisfiable 2.60s 1.53s
% Output   : Refutation 2.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   15 (   7 unt;   6 typ;   0 def)
%            Number of atoms       :   13 (   4 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   64 (   6   ~;   4   |;   0   &;  54   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :    6 (   0   ^;   6   !;   0   ?;   6   :)

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

thf(v_n_type,type,
    v_n: $i ).

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

thf(v_Y_type,type,
    v_Y: $i ).

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

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

thf(1,negated_conjecture,
    c_lessequals @ v_n @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(5,plain,
    c_lessequals @ v_n @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2,negated_conjecture,
    c_lessequals @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ v_n @ ( tc_set @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(6,plain,
    c_lessequals @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ v_n @ ( tc_set @ ( tc_set @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,negated_conjecture,
    ( v_n
   != ( c_Union @ v_Y @ ( tc_set @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(7,plain,
    ( v_n
   != ( c_Union @ v_Y @ ( tc_set @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(10,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)],[4]) ).

thf(13,plain,
    $false,
    inference(e,[status(thm)],[5,6,7,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET855-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 19:17:15 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.95/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.26/1.01  % [INFO] 	 Parsing done (116ms). 
% 1.26/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.59/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.59/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.26  % [INFO] 	 Found a conjecture and 1 axioms. Running axiom selection ... 
% 1.88/1.28  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.88/1.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.88/1.28  % [INFO] 	 Type checking passed. 
% 1.88/1.29  % [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 ... 
% 2.60/1.53  % External prover 'e' found a proof!
% 2.60/1.53  % [INFO] 	 Killing All external provers ... 
% 2.60/1.53  % Time passed: 1014ms (effective reasoning time: 510ms)
% 2.60/1.53  % 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)>
% 2.60/1.53  % Axioms used in derivation (1): cls_Set_Osubset__antisym_0
% 2.60/1.53  % No. of inferences in proof: 9
% 2.60/1.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1014 ms resp. 510 ms w/o parsing
% 2.60/1.55  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.60/1.55  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------