TSTP Solution File: LAT330+2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT330+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 11:27:54 EDT 2023

% Result   : ContradictoryAxioms 164.47s 32.53s
% Output   : Refutation 164.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   46 (  27 unt;   7 typ;   0 def)
%            Number of atoms       :   57 (  42 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  165 (  13   ~;   7   |;   2   &; 136   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 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   :   52 (   0   ^;  51   !;   1   ?;  52   :)

% Comments : 
%------------------------------------------------------------------------------
thf(k2_tarski_type,type,
    k2_tarski: $i > $i > $i ).

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

thf(k4_xboole_0_type,type,
    k4_xboole_0: $i > $i > $i ).

thf(k1_tarski_type,type,
    k1_tarski: $i > $i ).

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

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

thf(sk13_type,type,
    sk13: $i > $i > $i ).

thf(167,axiom,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
      = ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).

thf(1951,plain,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
      = ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(1952,plain,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
      = ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
    inference(cnf,[status(esa)],[1951]) ).

thf(1953,plain,
    ! [A: $i] :
      ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
      = ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
    inference(lifteq,[status(thm)],[1952]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).

thf(1232,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(1233,plain,
    ! [B: $i,A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1232]) ).

thf(1234,plain,
    ! [B: $i,A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1233]) ).

thf(37944,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k4_xboole_0 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
        = k1_xboole_0 )
      | ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
       != ( k2_tarski @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1953,1234]) ).

thf(37945,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[37944:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).

thf(38041,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[37945]) ).

thf(39,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
        = ( k4_xboole_0 @ B @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).

thf(1187,plain,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
        = ( k4_xboole_0 @ B @ A ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(1188,plain,
    ! [B: $i,A: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
       != ( k4_xboole_0 @ B @ A ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1187]) ).

thf(1189,plain,
    ! [B: $i,A: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
       != ( k4_xboole_0 @ B @ A ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[1188]) ).

thf(1190,plain,
    ! [B: $i,A: $i] :
      ( ( sk13 @ A @ ( k4_xboole_0 @ B @ A ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk13])]) ).

thf(39002,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk13 @ B @ k1_xboole_0 )
        = C )
      | ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
       != ( k4_xboole_0 @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[38041,1190]) ).

thf(39003,plain,
    ! [A: $i] :
      ( ( sk13 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
      = ( k1_tarski @ k1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[39002:[bind(A,$thf( F )),bind(B,$thf( k1_zfmisc_1 @ ( k1_tarski @ F ) )),bind(C,$thf( k1_tarski @ k1_xboole_0 ))]]) ).

thf(39166,plain,
    ! [A: $i] :
      ( ( sk13 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
      = ( k1_tarski @ k1_xboole_0 ) ),
    inference(simp,[status(thm)],[39003]) ).

thf(132,axiom,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).

thf(1800,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(1801,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1800]) ).

thf(1802,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1801]) ).

thf(36704,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk13 @ B @ k1_xboole_0 )
        = C )
      | ( ( k4_xboole_0 @ k1_xboole_0 @ A )
       != ( k4_xboole_0 @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1802,1190]) ).

thf(36705,plain,
    ! [A: $i] :
      ( ( sk13 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[36704:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(45344,plain,
    ( ( k1_tarski @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(rewrite,[status(thm)],[39166,36705]) ).

thf(330,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(2929,plain,
    ! [A: $i] :
      ( ( ( v1_xboole_0 @ A )
       => ( A = k1_xboole_0 ) )
      & ( ( A = k1_xboole_0 )
       => ( v1_xboole_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(2930,plain,
    ( ! [A: $i] :
        ( ( v1_xboole_0 @ A )
       => ( A = k1_xboole_0 ) )
    & ! [A: $i] :
        ( ( A = k1_xboole_0 )
       => ( v1_xboole_0 @ A ) ) ),
    inference(miniscope,[status(thm)],[2929]) ).

thf(2931,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( v1_xboole_0 @ A ) ),
    inference(cnf,[status(esa)],[2930]) ).

thf(2933,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( v1_xboole_0 @ A ) ),
    inference(lifteq,[status(thm)],[2931]) ).

thf(2934,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(simp,[status(thm)],[2933]) ).

thf(710,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(4828,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(4829,plain,
    ~ ? [A: $i] : ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    inference(miniscope,[status(thm)],[4828]) ).

thf(4830,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    inference(cnf,[status(esa)],[4829]) ).

thf(7518,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k1_tarski @ A ) )
     != ( v1_xboole_0 @ k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[2934,4830]) ).

thf(7527,plain,
    ! [A: $i] :
      ( ( k1_tarski @ A )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[7518]) ).

thf(45345,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[45344,7527]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : LAT330+2 : TPTP v8.1.2. Released v3.4.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n027.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 14:23:36 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.88/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.41/1.21  % [INFO] 	 Parsing done (376ms). 
% 2.41/1.22  % [INFO] 	 Running in sequential loop mode. 
% 2.85/1.42  % [INFO] 	 eprover registered as external prover. 
% 2.85/1.42  % [INFO] 	 cvc4 registered as external prover. 
% 2.85/1.42  % [INFO] 	 Scanning for conjecture ... 
% 3.71/1.62  % [INFO] 	 Found a conjecture and 3003 axioms. Running axiom selection ... 
% 4.97/2.05  % [INFO] 	 Axiom selection finished. Selected 1018 axioms (removed 1985 axioms). 
% 6.86/2.59  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 6.86/2.63  % [INFO] 	 Type checking passed. 
% 6.86/2.63  % [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 ... 
% 164.47/32.52  % [INFO] 	 Killing All external provers ... 
% 164.47/32.53  % Time passed: 32019ms (effective reasoning time: 31305ms)
% 164.47/32.53  % Axioms used in derivation (6): d5_xboole_0, fc2_subset_1, t22_zfmisc_1, t30_zfmisc_1, t4_boole, t32_xboole_1
% 164.47/32.53  % No. of inferences in proof: 39
% 164.47/32.53  % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 32019 ms resp. 31305 ms w/o parsing
% 164.47/32.57  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 164.47/32.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------