TSTP Solution File: ALG227+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ALG227+1 : TPTP v8.2.0. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 : Mon May 20 18:14:29 EDT 2024

% Result   : Theorem 3.44s 1.89s
% Output   : Refutation 3.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   65 (  11 unt;  13 typ;   0 def)
%            Number of atoms       :  150 (  21 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  334 (  27   ~;   2   |;  49   &; 209   @)
%                                         (   3 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :   86 (   0   ^  65   !;  21   ?;  86   :)

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

thf(m1_pboole_type,type,
    m1_pboole: $i > $i > $o ).

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

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

thf(k1_closure3_type,type,
    k1_closure3: $i > $i > $i ).

thf(k1_funct_1_type,type,
    k1_funct_1: $i > $i > $i ).

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

thf(v1_relat_1_type,type,
    v1_relat_1: $i > $o ).

thf(v1_funct_1_type,type,
    v1_funct_1: $i > $o ).

thf(v2_funct_1_type,type,
    v2_funct_1: $i > $o ).

thf(v1_fraenkel_type,type,
    v1_fraenkel: $i > $o ).

thf(a_2_0_closure3_type,type,
    a_2_0_closure3: $i > $i > $i ).

thf(v1_finset_1_type,type,
    v1_finset_1: $i > $o ).

thf(9,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(52,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_pboole @ B @ A )
         => ! [C: $i] :
              ( ( C
                = ( k1_closure3 @ A @ B ) )
            <=> ( C
                = ( a_2_0_closure3 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).

thf(106,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_pboole @ B @ A )
         => ! [C: $i] :
              ( ( ( C
                  = ( k1_closure3 @ A @ B ) )
               => ( C
                  = ( a_2_0_closure3 @ A @ B ) ) )
              & ( ( C
                  = ( a_2_0_closure3 @ A @ B ) )
               => ( C
                  = ( k1_closure3 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(4,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(38,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_fraenkel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_closure2) ).

thf(41,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_fraenkel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(34,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_pboole @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
               => ( ( k1_funct_1 @ B @ C )
                  = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_closure3) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ~ ( v1_xboole_0 @ A )
       => ! [B: $i] :
            ( ( m1_pboole @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
                 => ( ( k1_funct_1 @ B @ C )
                    = k1_xboole_0 ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(27,plain,
    ~ ! [A: $i] :
        ( ~ ( v1_xboole_0 @ A )
       => ! [B: $i] :
            ( ( m1_pboole @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
                 => ( ( k1_funct_1 @ B @ C )
                    = k1_xboole_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,axiom,
    v1_xboole_0 @ k1_xboole_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(66,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).

thf(80,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(48,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).

thf(67,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(43,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(25,axiom,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(114,plain,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(14,axiom,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_finset_1 @ A )
      & ( v1_fraenkel @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_closure2) ).

thf(69,plain,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_finset_1 @ A )
      & ( v1_fraenkel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
        <=> ( r2_hidden @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

thf(88,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ C @ B ) )
          & ( ( r2_hidden @ C @ B )
           => ( r2_hidden @ C @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

thf(46,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_pboole @ C @ B ) )
     => ( ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ B )
            & ( A = D )
            & ( ( k1_funct_1 @ C @ D )
             != k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).

thf(57,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_pboole @ C @ B ) )
     => ( ( ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( A = D )
              & ( ( k1_funct_1 @ C @ D )
               != k1_xboole_0 ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( A = D )
              & ( ( k1_funct_1 @ C @ D )
               != k1_xboole_0 ) )
         => ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(78,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(26,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(117,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(102,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(54,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(19,axiom,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(86,plain,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(15,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(76,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(98,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(18,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).

thf(83,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(22,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_pboole @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).

thf(100,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_pboole @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(121,plain,
    $false,
    inference(e,[status(thm)],[52,106,38,41,34,27,66,80,48,67,43,114,69,88,46,57,78,117,102,54,86,76,98,83,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : ALG227+1 : TPTP v8.2.0. Released v3.4.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n012.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sat May 18 23:01:24 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.86/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.04/0.92  % [INFO] 	 Parsing done (117ms). 
% 1.29/0.93  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.64/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.73/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ... 
% 1.89/1.30  % [INFO] 	 Axiom selection finished. Selected 24 axioms (removed 4 axioms). 
% 2.13/1.33  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.13/1.33  % [INFO] 	 Type checking passed. 
% 2.13/1.34  % [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 ... 
% 3.44/1.89  % External prover 'e' found a proof!
% 3.44/1.89  % [INFO] 	 Killing All external provers ... 
% 3.44/1.89  % Time passed: 1415ms (effective reasoning time: 955ms)
% 3.44/1.89  % Solved by 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)>
% 3.44/1.89  % Axioms used in derivation (24): d3_closure3, rc3_funct_1, t6_boole, t2_tarski, cc1_closure2, rc2_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, fraenkel_a_2_0_closure3, rc1_funct_1, t7_boole, cc1_funct_1, dt_m1_pboole, existence_m1_pboole, cc2_funct_1, existence_m1_subset_1, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, t2_subset, rc1_closure2
% 3.44/1.89  % No. of inferences in proof: 52
% 3.44/1.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1415 ms resp. 955 ms w/o parsing
% 3.70/1.95  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.70/1.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------