TSTP Solution File: NUN088+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : NUN088+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n031.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 11:46:19 EDT 2023

% Result   : Theorem 3.55s 1.83s
% Output   : Refutation 3.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   45 (   3 unt;   5 typ;   0 def)
%            Number of atoms       :  163 (   0 equ;   0 cnn)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  539 (  82   ~;  61   |;  62   &; 334   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   1 con; 0-3 aty)
%            Number of variables   :  143 (   0   ^; 103   !;  40   ?; 143   :)

% Comments : 
%------------------------------------------------------------------------------
thf(id_type,type,
    id: $i > $i > $o ).

thf(r1_type,type,
    r1: $i > $o ).

thf(r2_type,type,
    r2: $i > $i > $o ).

thf(r4_type,type,
    r4: $i > $i > $i > $o ).

thf(r3_type,type,
    r3: $i > $i > $i > $o ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( id @ A @ B )
      | ( ~ ( r1 @ A )
        & ~ ( r1 @ B ) )
      | ( ( r1 @ A )
        & ( r1 @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

thf(101,plain,
    ! [A: $i,B: $i] :
      ( ~ ( id @ A @ B )
      | ( ~ ( r1 @ A )
        & ~ ( r1 @ B ) )
      | ( ( r1 @ A )
        & ( r1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ~ ( id @ C @ B )
          | ~ ( r1 @ C ) )
      | ~ ( r2 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).

thf(52,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ~ ( id @ C @ B )
          | ~ ( r1 @ C ) )
      | ~ ( r2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(7,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( id @ B @ A )
      & ? [C: $i] :
          ( ( r1 @ C )
          & ( r3 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).

thf(46,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( id @ B @ A )
      & ? [C: $i] :
          ( ( r1 @ C )
          & ( r3 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ? [B: $i] :
          ( ( id @ A @ B )
          & ( r1 @ B ) )
      | ? [B: $i,C: $i] :
          ( ( id @ A @ C )
          & ( r2 @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6a) ).

thf(65,plain,
    ! [A: $i] :
      ( ? [B: $i] :
          ( ( id @ A @ B )
          & ( r1 @ B ) )
      | ? [B: $i,C: $i] :
          ( ( id @ A @ C )
          & ( r2 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(6,axiom,
    ? [A: $i] :
    ! [B: $i] :
      ( ( ( id @ B @ A )
        & ( r1 @ B ) )
      | ( ~ ( r1 @ B )
        & ~ ( id @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

thf(41,plain,
    ? [A: $i] :
    ! [B: $i] :
      ( ( ( id @ B @ A )
        & ( r1 @ B ) )
      | ( ~ ( r1 @ B )
        & ~ ( id @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ? [D: $i] :
          ( ( id @ D @ C )
          & ? [E: $i] :
              ( ( r2 @ B @ E )
              & ( r4 @ A @ E @ D ) ) )
      & ? [D: $i] :
          ( ( r3 @ D @ A @ C )
          & ( r4 @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).

thf(32,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ? [D: $i] :
          ( ( id @ D @ C )
          & ? [E: $i] :
              ( ( r2 @ B @ E )
              & ( r4 @ A @ E @ D ) ) )
      & ? [D: $i] :
          ( ( r3 @ D @ A @ C )
          & ( r4 @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ~ ( id @ A @ D )
      | ~ ( id @ B @ E )
      | ~ ( id @ C @ F )
      | ( ~ ( r3 @ A @ B @ C )
        & ~ ( r3 @ D @ E @ F ) )
      | ( ( r3 @ A @ B @ C )
        & ( r3 @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

thf(54,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ~ ( id @ A @ D )
      | ~ ( id @ B @ E )
      | ~ ( id @ C @ F )
      | ( ~ ( r3 @ A @ B @ C )
        & ~ ( r3 @ D @ E @ F ) )
      | ( ( r3 @ A @ B @ C )
        & ( r3 @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(15,axiom,
    ! [A: $i] : ( id @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

thf(81,plain,
    ! [A: $i] : ( id @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( id @ A @ C )
      | ~ ( id @ B @ D )
      | ( ~ ( r2 @ A @ B )
        & ~ ( r2 @ C @ D ) )
      | ( ( r2 @ A @ B )
        & ( r2 @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

thf(95,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( id @ A @ C )
      | ~ ( id @ B @ D )
      | ( ~ ( r2 @ A @ B )
        & ~ ( r2 @ C @ D ) )
      | ( ( r2 @ A @ B )
        & ( r2 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ! [D: $i] :
              ( ~ ( id @ D @ C )
              | ~ ( r2 @ A @ D ) )
          | ~ ( r2 @ B @ C ) )
      | ( id @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).

thf(50,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ! [D: $i] :
              ( ~ ( id @ D @ C )
              | ~ ( r2 @ A @ D ) )
          | ~ ( r2 @ B @ C ) )
      | ( id @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ~ ( id @ A @ D )
      | ~ ( id @ B @ E )
      | ~ ( id @ C @ F )
      | ( ~ ( r4 @ A @ B @ C )
        & ~ ( r4 @ D @ E @ F ) )
      | ( ( r4 @ A @ B @ C )
        & ( r4 @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

thf(26,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ~ ( id @ A @ D )
      | ~ ( id @ B @ E )
      | ~ ( id @ C @ F )
      | ( ~ ( r4 @ A @ B @ C )
        & ~ ( r4 @ D @ E @ F ) )
      | ( ( r4 @ A @ B @ C )
        & ( r4 @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ? [D: $i] :
          ( ( id @ D @ C )
          & ? [E: $i] :
              ( ( r2 @ B @ E )
              & ( r3 @ A @ E @ D ) ) )
      & ? [D: $i] :
          ( ( r2 @ D @ C )
          & ( r3 @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).

thf(75,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ? [D: $i] :
          ( ( id @ D @ C )
          & ? [E: $i] :
              ( ( r2 @ B @ E )
              & ( r3 @ A @ E @ D ) ) )
      & ? [D: $i] :
          ( ( r2 @ D @ C )
          & ( r3 @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(11,axiom,
    ! [A: $i] :
    ? [B: $i] :
    ! [C: $i] :
      ( ( ( id @ C @ B )
        & ( r2 @ A @ C ) )
      | ( ~ ( r2 @ A @ C )
        & ~ ( id @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

thf(60,plain,
    ! [A: $i] :
    ? [B: $i] :
    ! [C: $i] :
      ( ( ( id @ C @ B )
        & ( r2 @ A @ C ) )
      | ( ~ ( r2 @ A @ C )
        & ~ ( id @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
    ! [D: $i] :
      ( ( ( id @ D @ C )
        & ( r4 @ A @ B @ D ) )
      | ( ~ ( r4 @ A @ B @ D )
        & ~ ( id @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

thf(85,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
    ! [D: $i] :
      ( ( ( id @ D @ C )
        & ( r4 @ A @ B @ D ) )
      | ( ~ ( r4 @ A @ B @ D )
        & ~ ( id @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( id @ A @ B )
      | ( id @ A @ C )
      | ~ ( id @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

thf(38,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( id @ A @ B )
      | ( id @ A @ C )
      | ~ ( id @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(13,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ? [C: $i] :
          ( ( r1 @ C )
          & ( r4 @ A @ C @ B ) )
      & ? [C: $i] :
          ( ( id @ B @ C )
          & ( r1 @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).

thf(70,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ? [C: $i] :
          ( ( r1 @ C )
          & ( r4 @ A @ C @ B ) )
      & ? [C: $i] :
          ( ( id @ B @ C )
          & ( r1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ~ ( id @ B @ A )
          | ~ ( r1 @ B ) )
      | ! [B: $i] :
          ( ~ ( r1 @ B )
          | ~ ( r2 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zerounidone) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ! [B: $i] :
            ( ~ ( id @ B @ A )
            | ~ ( r1 @ B ) )
        | ! [B: $i] :
            ( ~ ( r1 @ B )
            | ~ ( r2 @ B @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(21,plain,
    ~ ! [A: $i] :
        ( ! [B: $i] :
            ( ~ ( id @ B @ A )
            | ~ ( r1 @ B ) )
        | ! [B: $i] :
            ( ~ ( r1 @ B )
            | ~ ( r2 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
    ! [D: $i] :
      ( ( ( id @ D @ C )
        & ( r3 @ A @ B @ D ) )
      | ( ~ ( r3 @ A @ B @ D )
        & ~ ( id @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(90,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
    ! [D: $i] :
      ( ( ( id @ D @ C )
        & ( r3 @ A @ B @ D ) )
      | ( ~ ( r3 @ A @ B @ D )
        & ~ ( id @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( id @ A @ B )
      | ( id @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

thf(83,plain,
    ! [A: $i,B: $i] :
      ( ~ ( id @ A @ B )
      | ( id @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(106,plain,
    $false,
    inference(e,[status(thm)],[101,52,46,65,41,32,54,81,95,50,26,75,60,85,38,70,21,90,83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUN088+1 : TPTP v8.1.2. Released v7.3.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n031.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 21:32:41 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.36/1.02  % [INFO] 	 Parsing done (141ms). 
% 1.36/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.79/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.80/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.28  % [INFO] 	 Found a conjecture and 18 axioms. Running axiom selection ... 
% 2.01/1.32  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 0 axioms). 
% 2.01/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.01/1.36  % [INFO] 	 Type checking passed. 
% 2.01/1.37  % [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 ... 
% 3.55/1.82  % External prover 'e' found a proof!
% 3.55/1.82  % [INFO] 	 Killing All external provers ... 
% 3.55/1.83  % Time passed: 1307ms (effective reasoning time: 800ms)
% 3.55/1.83  % 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)>
% 3.55/1.83  % Axioms used in derivation (18): axiom_7, axiom_10, axiom_1a, axiom_4a, axiom_2, axiom_6, axiom_3, axiom_7a, axiom_8, axiom_6a, axiom_5, axiom_3a, axiom_11, axiom_9, axiom_4, axiom_1, axiom_2a, axiom_5a
% 3.55/1.83  % No. of inferences in proof: 40
% 3.55/1.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1307 ms resp. 800 ms w/o parsing
% 3.94/1.92  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.94/1.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------