%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GEO057-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 20:05:40 EDT 2024

% Result   : Unsatisfiable 30.56s 5.64s
% Output   : Refutation 30.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (  14 unt;   3 typ;   0 def)
%            Number of atoms       :   16 (  15 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   59 (   6   ~;   1   |;   0   &;  52   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   2 con; 0-4 aty)
%            Number of variables   :   22 (   0   ^  22   !;   0   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
thf(u_type,type,
    u: $i ).

thf(reflection_type,type,
    reflection: $i > $i > $i ).

thf(extension_type,type,
    extension: $i > $i > $i > $i > $i ).

thf(1,negated_conjecture,
    ( u
   != ( reflection @ u @ u ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_extension_by_reflection) ).

thf(34,plain,
    ( u
   != ( reflection @ u @ u ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(35,plain,
    ( u
   != ( reflection @ u @ u ) ),
    inference(polarity_switch,[status(thm)],[34]) ).

thf(36,plain,
    ( ( reflection @ u @ u )
   != u ),
    inference(lifteq,[status(thm)],[35]) ).

thf(31,axiom,
    ! [B: $i,A: $i] :
      ( ( reflection @ A @ B )
      = ( extension @ A @ B @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflection) ).

thf(100,plain,
    ! [B: $i,A: $i] :
      ( ( reflection @ A @ B )
      = ( extension @ A @ B @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(101,plain,
    ! [B: $i,A: $i] :
      ( ( extension @ A @ B @ A @ B )
      = ( reflection @ A @ B ) ),
    inference(lifteq,[status(thm)],[100]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( extension @ B @ A @ C @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).

thf(88,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
      = ( extension @ B @ A @ C @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(89,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( extension @ B @ A @ C @ C )
      = A ),
    inference(lifteq,[status(thm)],[88]) ).

thf(4546,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( reflection @ A @ B )
        = C )
      | ( ( extension @ A @ B @ A @ B )
       != ( extension @ D @ C @ E @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[101,89]) ).

thf(4547,plain,
    ! [A: $i] :
      ( ( reflection @ A @ A )
      = A ),
    inference(pattern_uni,[status(thm)],[4546:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B )),bind(E,$thf( B ))]]) ).

thf(4561,plain,
    ! [A: $i] :
      ( ( reflection @ A @ A )
      = A ),
    inference(simp,[status(thm)],[4547]) ).

thf(4707,plain,
    u != u,
    inference(rewrite,[status(thm)],[36,4561]) ).

thf(4708,plain,
    $false,
    inference(simp,[status(thm)],[4707]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GEO057-3 : TPTP v8.2.0. Released v1.0.0.
% 0.12/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n014.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 : Sun May 19 15:09:09 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.83/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.97  % [INFO] 	 Parsing done (129ms). 
% 1.22/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.20  % [INFO] 	 nitpick registered as external prover. 
% 1.83/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.94/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ... 
% 1.94/1.29  % [INFO] 	 Axiom selection finished. Selected 32 axioms (removed 0 axioms). 
% 1.94/1.33  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.27/1.34  % [INFO] 	 Type checking passed. 
% 2.27/1.34  % [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 ... 
% 30.56/5.63  % [INFO] 	 Killing All external provers ... 
% 30.56/5.64  % Time passed: 5115ms (effective reasoning time: 4641ms)
% 30.56/5.64  % Axioms used in derivation (2): reflection, e1
% 30.56/5.64  % No. of inferences in proof: 15
% 30.56/5.64  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5115 ms resp. 4641 ms w/o parsing
% 30.56/5.68  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.56/5.68  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------