%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ALG267^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 : Mon May 20 18:14:39 EDT 2024

% Result   : Theorem 4.49s 1.98s
% Output   : Refutation 4.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   15 (   7 unt;   8 typ;   1 def)
%            Number of atoms       :    9 (   4 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   22 (   4   ~;   0   |;   0   &;  18   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    4 (   0   ^   3   !;   1   ?;   4   :)

% Comments : 
%------------------------------------------------------------------------------
thf(term_type,type,
    term: $tType ).

thf(subst_type,type,
    subst: $tType ).

thf(one_type,type,
    one: term ).

thf(sub_type,type,
    sub: term > subst > term ).

thf(sh_type,type,
    sh: subst ).

thf(push_type,type,
    push: term > subst > subst ).

thf(hoasinduction_lem3b_lthm_type,type,
    hoasinduction_lem3b_lthm: $o ).

thf(hoasinduction_lem3b_lthm_def,definition,
    hoasinduction_lem3b_lthm = hoasinduction_lem3b ).

thf(sk1_type,type,
    sk1: term ).

thf(1,conjecture,
    hoasinduction_lem3b_lthm,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ hoasinduction_lem3b_lthm,
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: term] :
      ? [B: subst > term > term] :
        ( ( sub @ A @ ( push @ one @ sh ) )
        = ( B @ sh @ one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ! [A: subst > term > term] :
      ( ( sub @ sk1 @ ( push @ one @ sh ) )
     != ( A @ sh @ one ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [A: subst > term > term] :
      ( ( sub @ sk1 @ ( push @ one @ sh ) )
     != ( A @ sh @ one ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    $false,
    inference(pre_uni,[status(thm)],[5:[bind(A,$thf( ^ [B: subst] : ^ [C: term] : ( sub @ sk1 @ ( push @ one @ sh ) ) ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG267^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n025.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 : Sat May 18 23:25:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.96/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.86/1.15  % [INFO] 	 Parsing done (218ms). 
% 1.86/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.45/1.37  % [INFO] 	 eprover registered as external prover. 
% 2.45/1.37  % [INFO] 	 cvc4 registered as external prover. 
% 2.45/1.37  % [INFO] 	 Scanning for conjecture ... 
% 3.37/1.66  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 3.37/1.67  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 3.57/1.68  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.57/1.68  % [INFO] 	 Type checking passed. 
% 3.57/1.68  % [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 ... 
% 4.49/1.98  % [INFO] 	 Killing All external provers ... 
% 4.49/1.98  % Time passed: 1425ms (effective reasoning time: 817ms)
% 4.49/1.98  % 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)>
% 4.49/1.98  % Axioms used in derivation (0): 
% 4.49/1.98  % No. of inferences in proof: 6
% 4.49/1.98  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1425 ms resp. 817 ms w/o parsing
% 4.49/2.00  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.49/2.00  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------