TSTP Solution File: REL003-1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : REL003-1 : TPTP v8.2.0. Released v4.0.0.
% 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 : Tue May 21 02:33:13 EDT 2024

% Result   : Unsatisfiable 37.94s 6.72s
% Output   : Refutation 37.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   27 (  11 unt;   4 typ;   0 def)
%            Number of atoms       :   35 (  34 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  143 (  14   ~;  12   |;   0   &; 117   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   10 (   0   ^  10   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
thf(join_type,type,
    join: $i > $i > $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(converse_type,type,
    converse: $i > $i ).

thf(1,negated_conjecture,
    ( ( ( join @ sk1 @ sk2 )
      = sk2 )
    | ( ( join @ ( converse @ sk1 ) @ ( converse @ sk2 ) )
      = ( converse @ sk2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).

thf(16,plain,
    ( ( ( join @ sk1 @ sk2 )
      = sk2 )
    | ( ( join @ ( converse @ sk1 ) @ ( converse @ sk2 ) )
      = ( converse @ sk2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(18,plain,
    ( ( ( join @ sk1 @ sk2 )
      = sk2 )
    | ( ( join @ ( converse @ sk1 ) @ ( converse @ sk2 ) )
      = ( converse @ sk2 ) ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(19,plain,
    ( ( ( join @ sk1 @ sk2 )
      = sk2 )
    | ( ( join @ ( converse @ sk1 ) @ ( converse @ sk2 ) )
      = ( converse @ sk2 ) ) ),
    inference(lifteq,[status(thm)],[18]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( converse @ ( join @ A @ B ) )
      = ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).

thf(38,plain,
    ! [B: $i,A: $i] :
      ( ( converse @ ( join @ A @ B ) )
      = ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(39,plain,
    ! [B: $i,A: $i] :
      ( ( join @ ( converse @ A ) @ ( converse @ B ) )
      = ( converse @ ( join @ A @ B ) ) ),
    inference(lifteq,[status(thm)],[38]) ).

thf(2900,plain,
    ( ( ( join @ sk1 @ sk2 )
      = sk2 )
    | ( ( converse @ ( join @ sk1 @ sk2 ) )
      = ( converse @ sk2 ) ) ),
    inference(rewrite,[status(thm)],[19,39]) ).

thf(2,negated_conjecture,
    ( ( ( join @ sk1 @ sk2 )
     != sk2 )
    | ( ( join @ ( converse @ sk1 ) @ ( converse @ sk2 ) )
     != ( converse @ sk2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).

thf(17,plain,
    ( ( ( join @ sk1 @ sk2 )
     != sk2 )
    | ( ( join @ ( converse @ sk1 ) @ ( converse @ sk2 ) )
     != ( converse @ sk2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(20,plain,
    ( ( ( join @ sk1 @ sk2 )
     != sk2 )
    | ( ( join @ ( converse @ sk1 ) @ ( converse @ sk2 ) )
     != ( converse @ sk2 ) ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(21,plain,
    ( ( ( join @ sk1 @ sk2 )
     != sk2 )
    | ( ( join @ ( converse @ sk1 ) @ ( converse @ sk2 ) )
     != ( converse @ sk2 ) ) ),
    inference(lifteq,[status(thm)],[20]) ).

thf(2898,plain,
    ( ( ( join @ sk1 @ sk2 )
     != sk2 )
    | ( ( converse @ ( join @ sk1 @ sk2 ) )
     != ( converse @ sk2 ) ) ),
    inference(rewrite,[status(thm)],[21,39]) ).

thf(5813,plain,
    ( ( ( join @ sk1 @ sk2 )
     != sk2 )
    | ( ( join @ sk1 @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[2898]) ).

thf(6122,plain,
    ( ( join @ sk1 @ sk2 )
   != sk2 ),
    inference(simp,[status(thm)],[5813]) ).

thf(6127,plain,
    ( ( converse @ ( join @ sk1 @ sk2 ) )
    = ( converse @ sk2 ) ),
    inference(simplifyReflect,[status(thm)],[2900,6122]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( converse @ ( converse @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).

thf(36,plain,
    ! [A: $i] :
      ( ( converse @ ( converse @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(37,plain,
    ! [A: $i] :
      ( ( converse @ ( converse @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[36]) ).

thf(6229,plain,
    ! [A: $i] :
      ( ( ( converse @ ( converse @ sk2 ) )
        = A )
      | ( ( converse @ ( join @ sk1 @ sk2 ) )
       != ( converse @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6127,37]) ).

thf(6230,plain,
    ( ( join @ sk1 @ sk2 )
    = ( converse @ ( converse @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[6229:[bind(A,$thf( join @ sk1 @ sk2 ))]]) ).

thf(6311,plain,
    ( ( join @ sk1 @ sk2 )
    = sk2 ),
    inference(rewrite,[status(thm)],[6230,37]) ).

thf(6312,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[6311,6122]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09  % Problem  : REL003-1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.30  % Computer : n029.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit : 300
% 0.11/0.30  % WCLimit  : 300
% 0.11/0.30  % DateTime : Mon May 20 08:09:54 EDT 2024
% 0.11/0.30  % CPUTime  : 
% 0.79/0.79  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.94/0.93  % [INFO] 	 Parsing done (140ms). 
% 1.19/0.94  % [INFO] 	 Running in sequential loop mode. 
% 1.56/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.56/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ... 
% 1.77/1.26  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 1.77/1.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.77/1.28  % [INFO] 	 Type checking passed. 
% 1.77/1.29  % [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 ... 
% 37.94/6.71  % [INFO] 	 Killing All external provers ... 
% 37.94/6.71  % Time passed: 6260ms (effective reasoning time: 5766ms)
% 37.94/6.72  % Axioms used in derivation (2): converse_additivity_9, converse_idempotence_8
% 37.94/6.72  % No. of inferences in proof: 23
% 37.94/6.72  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6260 ms resp. 5766 ms w/o parsing
% 37.94/6.77  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 37.94/6.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------