TSTP Solution File: LAT299+2 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : LAT299+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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  7 07:53:07 EDT 2024

% Result   : ContradictoryAxioms 124.13s 23.59s
% Output   : Refutation 124.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   44 (  17 unt;   7 typ;   0 def)
%            Number of atoms       :   70 (  52 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  139 (  18   ~;  16   |;   4   &;  92   @)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   59 (   0   ^  56   !;   3   ?;  59   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v1_xboole_0_type,type,
    v1_xboole_0: $i > $o ).

thf(k2_zfmisc_1_type,type,
    k2_zfmisc_1: $i > $i > $i ).

thf(m1_subset_1_type,type,
    m1_subset_1: $i > $i > $o ).

thf(k1_xboole_0_type,type,
    k1_xboole_0: $i ).

thf(k1_zfmisc_1_type,type,
    k1_zfmisc_1: $i > $i ).

thf(sk43_type,type,
    sk43: $i > $i > $i ).

thf(sk102_type,type,
    sk102: $i > $i ).

thf(250,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(1756,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(1757,plain,
    ! [A: $i] : ( v1_xboole_0 @ ( sk102 @ A ) ),
    inference(cnf,[status(esa)],[1756]) ).

thf(281,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(1898,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(1899,plain,
    ~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(miniscope,[status(thm)],[1898]) ).

thf(1900,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(cnf,[status(esa)],[1899]) ).

thf(18820,plain,
    ! [B: $i,A: $i] :
      ( ( v1_xboole_0 @ ( sk102 @ A ) )
     != ( v1_xboole_0 @ ( k1_zfmisc_1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1757,1900]) ).

thf(18865,plain,
    ! [B: $i,A: $i] :
      ( ( sk102 @ A )
     != ( k1_zfmisc_1 @ B ) ),
    inference(simp,[status(thm)],[18820]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

thf(716,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(717,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      | ( A = k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[716]) ).

thf(718,plain,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
      | ~ ( v1_xboole_0 @ A ) ),
    inference(lifteq,[status(thm)],[717]) ).

thf(18834,plain,
    ! [B: $i,A: $i] :
      ( ( B = k1_xboole_0 )
      | ( ( v1_xboole_0 @ ( sk102 @ A ) )
       != ( v1_xboole_0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1757,718]) ).

thf(18835,plain,
    ! [A: $i] :
      ( ( sk102 @ A )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[18834:[bind(A,$thf( C )),bind(B,$thf( sk102 @ C ))]]) ).

thf(18881,plain,
    ! [A: $i] :
      ( ( sk102 @ A )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[18835]) ).

thf(25456,plain,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ A )
     != k1_xboole_0 ),
    inference(rewrite,[status(thm)],[18865,18881]) ).

thf(73,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ B )
        = k1_xboole_0 )
    <=> ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).

thf(982,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( k2_zfmisc_1 @ A @ B )
          = k1_xboole_0 )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 ) ) )
      & ( ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 ) )
       => ( ( k2_zfmisc_1 @ A @ B )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(983,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( k2_zfmisc_1 @ A @ B )
          = k1_xboole_0 )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 ) )
       => ( ( k2_zfmisc_1 @ A @ B )
          = k1_xboole_0 ) ) ),
    inference(miniscope,[status(thm)],[982]) ).

thf(985,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( ( k2_zfmisc_1 @ A @ B )
        = k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[983]) ).

thf(989,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( ( k2_zfmisc_1 @ A @ B )
        = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[985]) ).

thf(990,plain,
    ! [A: $i] :
      ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[989]) ).

thf(105,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ A )
        = ( k2_zfmisc_1 @ B @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).

thf(1124,plain,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ A )
        = ( k2_zfmisc_1 @ B @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(1125,plain,
    ! [B: $i,A: $i] :
      ( ( ( k2_zfmisc_1 @ A @ A )
       != ( k2_zfmisc_1 @ B @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1124]) ).

thf(1126,plain,
    ! [B: $i,A: $i] :
      ( ( ( k2_zfmisc_1 @ A @ A )
       != ( k2_zfmisc_1 @ B @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[1125]) ).

thf(1127,plain,
    ! [B: $i,A: $i] :
      ( ( sk43 @ A @ ( k2_zfmisc_1 @ B @ A ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(k2_zfmisc_1),[sk43])]) ).

thf(33186,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk43 @ B @ k1_xboole_0 )
        = C )
      | ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
       != ( k2_zfmisc_1 @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[990,1127]) ).

thf(33187,plain,
    ! [A: $i] :
      ( ( sk43 @ k1_xboole_0 @ k1_xboole_0 )
      = A ),
    inference(pattern_uni,[status(thm)],[33186:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).

thf(984,plain,
    ! [B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( k2_zfmisc_1 @ A @ B )
        = k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[983]) ).

thf(987,plain,
    ! [B: $i,A: $i] :
      ( ( A != k1_xboole_0 )
      | ( ( k2_zfmisc_1 @ A @ B )
        = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[984]) ).

thf(988,plain,
    ! [A: $i] :
      ( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[987]) ).

thf(33160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk43 @ B @ k1_xboole_0 )
        = C )
      | ( ( k2_zfmisc_1 @ k1_xboole_0 @ A )
       != ( k2_zfmisc_1 @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[988,1127]) ).

thf(33161,plain,
    ! [A: $i] :
      ( ( sk43 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[33160:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(33303,plain,
    ! [A: $i] : ( k1_xboole_0 = A ),
    inference(rewrite,[status(thm)],[33187,33161]) ).

thf(33309,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[25456,33303]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LAT299+2 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon May  6 11:05:09 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.76/0.76  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.99/1.15  % [INFO] 	 Parsing done (386ms). 
% 2.31/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.84/1.37  % [INFO] 	 eprover registered as external prover. 
% 2.84/1.37  % [INFO] 	 cvc4 registered as external prover. 
% 2.84/1.38  % [INFO] 	 Scanning for conjecture ... 
% 3.54/1.57  % [INFO] 	 Found a conjecture and 2934 axioms. Running axiom selection ... 
% 4.99/1.98  % [INFO] 	 Axiom selection finished. Selected 667 axioms (removed 2267 axioms). 
% 6.36/2.39  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 6.54/2.42  % [INFO] 	 Type checking passed. 
% 6.54/2.42  % [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 ... 
% 124.13/23.58  % [INFO] 	 Killing All external provers ... 
% 124.13/23.59  % Time passed: 23118ms (effective reasoning time: 22422ms)
% 124.13/23.59  % Axioms used in derivation (5): t113_zfmisc_1, t115_zfmisc_1, fc1_subset_1, t6_boole, rc2_subset_1
% 124.13/23.59  % No. of inferences in proof: 37
% 124.13/23.59  % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 23118 ms resp. 22422 ms w/o parsing
% 124.13/23.61  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 124.13/23.61  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------