TSTP Solution File: LAT337+2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT337+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 11:27:58 EDT 2023

% Result   : ContradictoryAxioms 159.96s 35.52s
% Output   : Refutation 159.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   51 (  31 unt;   7 typ;   0 def)
%            Number of atoms       :   63 (  48 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  179 (  16   ~;   8   |;   2   &; 146   @)
%                                         (   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   :   53 (   0   ^;  52   !;   1   ?;  53   :)

% 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(sk14_type,type,
    sk14: $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/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).

thf(1967,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(1968,plain,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
      = ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
    inference(cnf,[status(esa)],[1967]) ).

thf(1969,plain,
    ! [A: $i] :
      ( ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) )
      = ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) ),
    inference(lifteq,[status(thm)],[1968]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).

thf(1256,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(1257,plain,
    ! [B: $i,A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1256]) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1257]) ).

thf(57273,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)],[1969,1258]) ).

thf(57274,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[57273:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( k1_tarski @ D ))]]) ).

thf(57476,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[57274]) ).

thf(39,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
        = ( k4_xboole_0 @ B @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).

thf(1211,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(1212,plain,
    ! [B: $i,A: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
       != ( k4_xboole_0 @ B @ A ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[1211]) ).

thf(1213,plain,
    ! [B: $i,A: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
       != ( k4_xboole_0 @ B @ A ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[1212]) ).

thf(1214,plain,
    ! [B: $i,A: $i] :
      ( ( sk14 @ A @ ( k4_xboole_0 @ B @ A ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk14])]) ).

thf(57587,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk14 @ 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)],[57476,1214]) ).

thf(57588,plain,
    ! [A: $i] :
      ( ( sk14 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
      = ( k1_tarski @ k1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[57587:[bind(A,$thf( F )),bind(B,$thf( k1_zfmisc_1 @ ( k1_tarski @ F ) )),bind(C,$thf( k1_tarski @ k1_xboole_0 ))]]) ).

thf(57845,plain,
    ! [A: $i] :
      ( ( sk14 @ ( k1_zfmisc_1 @ ( k1_tarski @ A ) ) @ k1_xboole_0 )
      = ( k1_tarski @ k1_xboole_0 ) ),
    inference(simp,[status(thm)],[57588]) ).

thf(132,axiom,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).

thf(1824,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(1825,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1824]) ).

thf(1826,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1825]) ).

thf(36330,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk14 @ B @ k1_xboole_0 )
        = C )
      | ( ( k4_xboole_0 @ k1_xboole_0 @ A )
       != ( k4_xboole_0 @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1826,1214]) ).

thf(36331,plain,
    ! [A: $i] :
      ( ( sk14 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[36330:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(58225,plain,
    ( ( k1_tarski @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(rewrite,[status(thm)],[57845,36331]) ).

thf(145,axiom,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).

thf(1882,plain,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(1883,plain,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1882]) ).

thf(323,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(2864,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)],[323]) ).

thf(2865,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)],[2864]) ).

thf(2866,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( v1_xboole_0 @ A ) ),
    inference(cnf,[status(esa)],[2865]) ).

thf(2868,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( v1_xboole_0 @ A ) ),
    inference(lifteq,[status(thm)],[2866]) ).

thf(2869,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(simp,[status(thm)],[2868]) ).

thf(491,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(3690,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(3691,plain,
    ~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(miniscope,[status(thm)],[3690]) ).

thf(3692,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(cnf,[status(esa)],[3691]) ).

thf(7864,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
     != ( v1_xboole_0 @ k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[2869,3692]) ).

thf(7873,plain,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ A )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[7864]) ).

thf(11187,plain,
    ! [A: $i] :
      ( ( ( k1_tarski @ k1_xboole_0 )
       != k1_xboole_0 )
      | ( ( k1_zfmisc_1 @ k1_xboole_0 )
       != ( k1_zfmisc_1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1883,7873]) ).

thf(11188,plain,
    ( ( k1_tarski @ k1_xboole_0 )
   != k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[11187:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(58226,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[58225,11188]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT337+2 : TPTP v8.1.2. Released v3.4.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n015.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 14:56:38 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.53/1.25  % [INFO] 	 Parsing done (382ms). 
% 2.53/1.26  % [INFO] 	 Running in sequential loop mode. 
% 3.03/1.46  % [INFO] 	 eprover registered as external prover. 
% 3.03/1.47  % [INFO] 	 cvc4 registered as external prover. 
% 3.03/1.47  % [INFO] 	 Scanning for conjecture ... 
% 3.90/1.69  % [INFO] 	 Found a conjecture and 3025 axioms. Running axiom selection ... 
% 5.25/2.12  % [INFO] 	 Axiom selection finished. Selected 1040 axioms (removed 1985 axioms). 
% 6.80/2.66  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 7.01/2.70  % [INFO] 	 Type checking passed. 
% 7.01/2.70  % [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 ... 
% 159.96/35.51  % [INFO] 	 Killing All external provers ... 
% 159.96/35.52  % Time passed: 34984ms (effective reasoning time: 34250ms)
% 159.96/35.52  % Axioms used in derivation (7): d5_xboole_0, t1_zfmisc_1, fc1_subset_1, t22_zfmisc_1, t30_zfmisc_1, t4_boole, t32_xboole_1
% 159.96/35.52  % No. of inferences in proof: 44
% 159.96/35.52  % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 34984 ms resp. 34250 ms w/o parsing
% 159.96/35.54  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 159.96/35.54  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------