TSTP Solution File: SEU450+2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU450+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n001.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 11:59:17 EDT 2023

% Result   : ContradictoryAxioms 55.96s 12.17s
% Output   : Refutation 55.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   45 (  26 unt;   7 typ;   0 def)
%            Number of atoms       :   56 (  41 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  148 (  13   ~;   7   |;   2   &; 119   @)
%                                         (   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   :   47 (   0   ^;  46   !;   1   ?;  47   :)

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

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

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

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

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

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

thf(sk6_type,type,
    sk6: $i > $i > $i ).

thf(79,axiom,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).

thf(1247,plain,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(1248,plain,
    ( ( k1_tarski @ k1_xboole_0 )
    = ( k1_zfmisc_1 @ k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1247]) ).

thf(23,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(980,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)],[23]) ).

thf(981,plain,
    ! [B: $i,A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[980]) ).

thf(982,plain,
    ! [B: $i,A: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[981]) ).

thf(10855,plain,
    ! [B: $i,A: $i] :
      ( ( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k2_tarski @ A @ B ) )
        = k1_xboole_0 )
      | ( ( k1_tarski @ k1_xboole_0 )
       != ( k1_tarski @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1248,982]) ).

thf(10856,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k2_tarski @ k1_xboole_0 @ A ) )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[10855:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(10918,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k2_tarski @ k1_xboole_0 @ A ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[10856]) ).

thf(18,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(958,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)],[18]) ).

thf(959,plain,
    ! [B: $i,A: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
       != ( k4_xboole_0 @ B @ A ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[958]) ).

thf(960,plain,
    ! [B: $i,A: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
       != ( k4_xboole_0 @ B @ A ) )
      | ( A = B ) ),
    inference(lifteq,[status(thm)],[959]) ).

thf(961,plain,
    ! [B: $i,A: $i] :
      ( ( sk6 @ A @ ( k4_xboole_0 @ B @ A ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(k4_xboole_0),[sk6])]) ).

thf(11760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk6 @ B @ k1_xboole_0 )
        = C )
      | ( ( k4_xboole_0 @ ( k1_zfmisc_1 @ k1_xboole_0 ) @ ( k2_tarski @ k1_xboole_0 @ A ) )
       != ( k4_xboole_0 @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10918,961]) ).

thf(11761,plain,
    ! [A: $i] :
      ( ( sk6 @ ( k2_tarski @ k1_xboole_0 @ A ) @ k1_xboole_0 )
      = ( k1_zfmisc_1 @ k1_xboole_0 ) ),
    inference(pattern_uni,[status(thm)],[11760:[bind(A,$thf( F )),bind(B,$thf( k2_tarski @ k1_xboole_0 @ F )),bind(C,$thf( k1_zfmisc_1 @ k1_xboole_0 ))]]) ).

thf(11852,plain,
    ! [A: $i] :
      ( ( sk6 @ ( k2_tarski @ k1_xboole_0 @ A ) @ k1_xboole_0 )
      = ( k1_zfmisc_1 @ k1_xboole_0 ) ),
    inference(simp,[status(thm)],[11761]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).

thf(1159,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(1160,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1159]) ).

thf(1161,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1160]) ).

thf(6627,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( sk6 @ B @ k1_xboole_0 )
        = C )
      | ( ( k4_xboole_0 @ k1_xboole_0 @ A )
       != ( k4_xboole_0 @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1161,961]) ).

thf(6628,plain,
    ! [A: $i] :
      ( ( sk6 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[6627:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(12378,plain,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(rewrite,[status(thm)],[11852,6628]) ).

thf(671,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(4200,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)],[671]) ).

thf(4201,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)],[4200]) ).

thf(4202,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( v1_xboole_0 @ A ) ),
    inference(cnf,[status(esa)],[4201]) ).

thf(4204,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
      | ( v1_xboole_0 @ A ) ),
    inference(lifteq,[status(thm)],[4202]) ).

thf(4205,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(simp,[status(thm)],[4204]) ).

thf(471,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(3116,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(3117,plain,
    ~ ? [A: $i] : ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(miniscope,[status(thm)],[3116]) ).

thf(3118,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(cnf,[status(esa)],[3117]) ).

thf(5286,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) )
     != ( v1_xboole_0 @ k1_xboole_0 ) ),
    inference(paramod_ordered,[status(thm)],[4205,3118]) ).

thf(5288,plain,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ A )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[5286]) ).

thf(12379,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[12378,5288]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : SEU450+2 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.34  % Computer : n001.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 13:24:05 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.94/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.65/1.27  % [INFO] 	 Parsing done (449ms). 
% 2.65/1.28  % [INFO] 	 Running in sequential loop mode. 
% 3.16/1.48  % [INFO] 	 eprover registered as external prover. 
% 3.16/1.48  % [INFO] 	 cvc4 registered as external prover. 
% 3.16/1.48  % [INFO] 	 Scanning for conjecture ... 
% 3.95/1.72  % [INFO] 	 Found a conjecture and 4535 axioms. Running axiom selection ... 
% 5.94/2.27  % [INFO] 	 Axiom selection finished. Selected 901 axioms (removed 3634 axioms). 
% 7.61/2.73  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 7.77/2.77  % [INFO] 	 Type checking passed. 
% 7.77/2.77  % [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 ... 
% 55.96/12.16  % [INFO] 	 Killing All external provers ... 
% 55.96/12.17  % Time passed: 11653ms (effective reasoning time: 10873ms)
% 55.96/12.17  % Axioms used in derivation (6): d5_xboole_0, t1_zfmisc_1, fc1_subset_1, t22_zfmisc_1, t4_boole, t32_xboole_1
% 55.96/12.17  % No. of inferences in proof: 38
% 55.96/12.17  % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11653 ms resp. 10873 ms w/o parsing
% 55.96/12.19  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 55.96/12.19  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------