TSTP Solution File: LAT318+2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT318+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 11:27:45 EDT 2023

% Result   : ContradictoryAxioms 63.15s 12.92s
% Output   : Refutation 63.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   42 (  11 unt;   9 typ;   0 def)
%            Number of atoms       :  116 (  40 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  337 (  44   ~;  14   |;  44   &; 214   @)
%                                         (   1 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   2 con; 0-2 aty)
%            Number of variables   :   90 (   0   ^;  80   !;  10   ?;  90   :)

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

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

thf(r1_tarski_type,type,
    r1_tarski: $i > $i > $o ).

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

thf(r2_hidden_type,type,
    r2_hidden: $i > $i > $o ).

thf(r2_tarski_type,type,
    r2_tarski: $i > $i > $o ).

thf(sk7_type,type,
    sk7: $i > $i > $i ).

thf(sk25_type,type,
    sk25: $i > $i ).

thf(sk157_type,type,
    sk157: $i > $i ).

thf(64,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(861,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)],[64]) ).

thf(862,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)],[861]) ).

thf(864,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( ( k2_zfmisc_1 @ A @ B )
        = k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[862]) ).

thf(868,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( ( k2_zfmisc_1 @ A @ B )
        = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[864]) ).

thf(869,plain,
    ! [A: $i] :
      ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[868]) ).

thf(16,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(683,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)],[16]) ).

thf(684,plain,
    ! [B: $i,A: $i] :
      ( ( ( k2_zfmisc_1 @ A @ A )
       != ( k2_zfmisc_1 @ B @ B ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[683]) ).

thf(685,plain,
    ! [B: $i,A: $i] :
      ( ( ( k2_zfmisc_1 @ A @ A )
       != ( k2_zfmisc_1 @ B @ B ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[684]) ).

thf(686,plain,
    ! [B: $i,A: $i] :
      ( ( sk7 @ A @ ( k2_zfmisc_1 @ B @ A ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(k2_zfmisc_1),[sk7])]) ).

thf(11793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk7 @ B @ k1_xboole_0 )
        = C )
      | ( ( k2_zfmisc_1 @ A @ k1_xboole_0 )
       != ( k2_zfmisc_1 @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[869,686]) ).

thf(11794,plain,
    ! [A: $i] :
      ( ( sk7 @ k1_xboole_0 @ k1_xboole_0 )
      = A ),
    inference(pattern_uni,[status(thm)],[11793:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).

thf(90,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( r2_hidden @ A @ B )
      & ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ B )
            & ( r1_tarski @ D @ C ) )
         => ( r2_hidden @ D @ B ) )
      & ! [C: $i] :
          ~ ( ( r2_hidden @ C @ B )
            & ! [D: $i] :
                ~ ( ( r2_hidden @ D @ B )
                  & ! [E: $i] :
                      ( ( r1_tarski @ E @ C )
                     => ( r2_hidden @ E @ D ) ) ) )
      & ! [C: $i] :
          ~ ( ( r1_tarski @ C @ B )
            & ~ ( r2_tarski @ C @ B )
            & ~ ( r2_hidden @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).

thf(994,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( r2_hidden @ A @ B )
      & ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ B )
            & ( r1_tarski @ D @ C ) )
         => ( r2_hidden @ D @ B ) )
      & ! [C: $i] :
          ~ ( ( r2_hidden @ C @ B )
            & ! [D: $i] :
                ~ ( ( r2_hidden @ D @ B )
                  & ! [E: $i] :
                      ( ( r1_tarski @ E @ C )
                     => ( r2_hidden @ E @ D ) ) ) )
      & ! [C: $i] :
          ~ ( ( r1_tarski @ C @ B )
            & ~ ( r2_tarski @ C @ B )
            & ~ ( r2_hidden @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(995,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( r2_hidden @ A @ B )
      & ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ B )
            & ( r1_tarski @ D @ C ) )
         => ( r2_hidden @ D @ B ) )
      & ~ ? [C: $i] :
            ( ( r2_hidden @ C @ B )
            & ~ ? [D: $i] :
                  ( ( r2_hidden @ D @ B )
                  & ! [E: $i] :
                      ( ( r1_tarski @ E @ C )
                     => ( r2_hidden @ E @ D ) ) ) )
      & ~ ? [C: $i] :
            ( ( r1_tarski @ C @ B )
            & ~ ( r2_tarski @ C @ B )
            & ~ ( r2_hidden @ C @ B ) ) ),
    inference(miniscope,[status(thm)],[994]) ).

thf(998,plain,
    ! [A: $i] : ( r2_hidden @ A @ ( sk25 @ A ) ),
    inference(cnf,[status(esa)],[995]) ).

thf(409,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( r2_hidden @ A @ B )
      & ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ B )
            & ( r1_tarski @ D @ C ) )
         => ( r2_hidden @ D @ B ) )
      & ! [C: $i] :
          ( ( r2_hidden @ C @ B )
         => ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
      & ! [C: $i] :
          ~ ( ( r1_tarski @ C @ B )
            & ~ ( r2_tarski @ C @ B )
            & ~ ( r2_hidden @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).

thf(2479,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( r2_hidden @ A @ B )
      & ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ B )
            & ( r1_tarski @ D @ C ) )
         => ( r2_hidden @ D @ B ) )
      & ! [C: $i] :
          ( ( r2_hidden @ C @ B )
         => ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
      & ! [C: $i] :
          ~ ( ( r1_tarski @ C @ B )
            & ~ ( r2_tarski @ C @ B )
            & ~ ( r2_hidden @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(2480,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( r2_hidden @ A @ B )
      & ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ B )
            & ( r1_tarski @ D @ C ) )
         => ( r2_hidden @ D @ B ) )
      & ! [C: $i] :
          ( ( r2_hidden @ C @ B )
         => ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
      & ~ ? [C: $i] :
            ( ( r1_tarski @ C @ B )
            & ~ ( r2_tarski @ C @ B )
            & ~ ( r2_hidden @ C @ B ) ) ),
    inference(miniscope,[status(thm)],[2479]) ).

thf(2484,plain,
    ! [A: $i] : ( r2_hidden @ A @ ( sk157 @ A ) ),
    inference(cnf,[status(esa)],[2480]) ).

thf(251,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(1751,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(1752,plain,
    ! [B: $i,A: $i] :
      ( ~ ( r2_hidden @ A @ B )
      | ~ ( r2_hidden @ B @ A ) ),
    inference(cnf,[status(esa)],[1751]) ).

thf(10060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( r2_hidden @ C @ B )
      | ( ( r2_hidden @ A @ ( sk157 @ A ) )
       != ( r2_hidden @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[2484,1752]) ).

thf(10061,plain,
    ! [A: $i] :
      ~ ( r2_hidden @ ( sk157 @ A ) @ A ),
    inference(pattern_uni,[status(thm)],[10060:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk157 @ D ))]]) ).

thf(10082,plain,
    ! [A: $i] :
      ~ ( r2_hidden @ ( sk157 @ A ) @ A ),
    inference(simp,[status(thm)],[10061]) ).

thf(11003,plain,
    ! [B: $i,A: $i] :
      ( ( r2_hidden @ A @ ( sk25 @ A ) )
     != ( r2_hidden @ ( sk157 @ B ) @ B ) ),
    inference(paramod_ordered,[status(thm)],[998,10082]) ).

thf(11016,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( sk157 @ B ) )
      | ( ( sk25 @ A )
       != B ) ),
    inference(simp,[status(thm)],[11003]) ).

thf(11022,plain,
    ! [A: $i] :
      ( ( sk25 @ ( sk157 @ A ) )
     != A ),
    inference(simp,[status(thm)],[11016]) ).

thf(12161,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk7 @ k1_xboole_0 @ k1_xboole_0 )
       != B )
      | ( A
       != ( sk25 @ ( sk157 @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11794,11022]) ).

thf(12162,plain,
    ! [A: $i] :
      ( ( sk7 @ k1_xboole_0 @ k1_xboole_0 )
     != A ),
    inference(pattern_uni,[status(thm)],[12161:[bind(A,$thf( sk25 @ ( sk157 @ D ) )),bind(B,$thf( D ))]]) ).

thf(12334,plain,
    $false,
    inference(simp,[status(thm)],[12162]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : LAT318+2 : TPTP v8.1.2. Released v3.4.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n017.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 13:47:32 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.66/1.31  % [INFO] 	 Parsing done (457ms). 
% 2.66/1.32  % [INFO] 	 Running in sequential loop mode. 
% 3.32/1.54  % [INFO] 	 eprover registered as external prover. 
% 3.32/1.55  % [INFO] 	 cvc4 registered as external prover. 
% 3.32/1.55  % [INFO] 	 Scanning for conjecture ... 
% 3.81/1.74  % [INFO] 	 Found a conjecture and 2985 axioms. Running axiom selection ... 
% 5.22/2.10  % [INFO] 	 Axiom selection finished. Selected 621 axioms (removed 2364 axioms). 
% 6.48/2.49  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 6.62/2.52  % [INFO] 	 Type checking passed. 
% 6.62/2.53  % [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 ... 
% 63.15/12.91  % [INFO] 	 Killing All external provers ... 
% 63.15/12.91  % Time passed: 12387ms (effective reasoning time: 11590ms)
% 63.15/12.92  % Axioms used in derivation (5): t113_zfmisc_1, t115_zfmisc_1, t136_zfmisc_1, t9_tarski, antisymmetry_r2_hidden
% 63.15/12.92  % No. of inferences in proof: 33
% 63.15/12.92  % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 12387 ms resp. 11590 ms w/o parsing
% 63.15/12.94  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.15/12.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------