TSTP Solution File: LCL688+1.001 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LCL688+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 11:31:16 EDT 2023

% Result   : Theorem 78.37s 13.41s
% Output   : Refutation 78.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   13 (   3 unt;   5 typ;   0 def)
%            Number of atoms       :  141 (   0 equ;   0 cnn)
%            Maximal formula atoms :   44 (  17 avg)
%            Number of connectives :  538 ( 176   ~; 114   |;  17   &; 229   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (  14 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   92 (   0   ^;  89   !;   3   ?;  92   :)

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

thf(p4_type,type,
    p4: $i > $o ).

thf(p3_type,type,
    p3: $i > $o ).

thf(p2_type,type,
    p2: $i > $o ).

thf(p1_type,type,
    p1: $i > $o ).

thf(1,conjecture,
    ~ ? [A: $i] :
        ~ ( ~ ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( p4 @ B ) )
          | ~ ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ( ~ ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ~ ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ! [E: $i] :
                                    ( ~ ( r1 @ D @ E )
                                    | ( p3 @ E ) )
                                | ~ ( p2 @ D ) ) )
                    | ~ ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ~ ( ~ ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ~ ( ! [E: $i] :
                                            ( ~ ( r1 @ D @ E )
                                            | ( p3 @ E ) )
                                        | ~ ( p2 @ D ) ) )
                              & ( p2 @ C )
                              & ~ ! [D: $i] :
                                    ( ~ ( r1 @ C @ D )
                                    | ~ ! [E: $i] :
                                          ( ~ ( r1 @ D @ E )
                                          | ~ ! [F: $i] :
                                                ( ~ ( r1 @ E @ F )
                                                | ~ ( p2 @ F ) ) ) ) ) ) ) )
          | ( ~ ( p1 @ A )
            & ~ ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ( p1 @ C ) ) )
            & ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ( p1 @ B )
                | ~ ! [C: $i] :
                      ( ~ ( r1 @ B @ C )
                      | ~ ( ~ ! [D: $i] :
                                ( ~ ( r1 @ C @ D )
                                | ( p1 @ D ) )
                          & ( p1 @ C ) ) ) ) )
          | ! [B: $i] :
              ( ~ ( r1 @ A @ B )
              | ! [C: $i] :
                  ( ~ ( r1 @ B @ C )
                  | ~ ! [D: $i] :
                        ( ~ ( r1 @ C @ D )
                        | ( p1 @ D ) ) )
              | ! [C: $i] :
                  ( ~ ( r1 @ B @ C )
                  | ( p1 @ C ) ) )
          | ! [B: $i] :
              ( ~ ( r1 @ A @ B )
              | ~ ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ~ ! [D: $i] :
                          ( ~ ( r1 @ C @ D )
                          | ( p2 @ D ) ) ) )
          | ~ ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ! [D: $i] :
                        ( ~ ( r1 @ C @ D )
                        | ~ ( p1 @ D ) ) )
                | ~ ! [C: $i] :
                      ( ~ ( r1 @ B @ C )
                      | ~ ( p1 @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).

thf(2,negated_conjecture,
    ~ ~ ? [A: $i] :
          ~ ( ~ ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( p4 @ B ) )
            | ~ ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( ~ ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ! [E: $i] :
                                      ( ~ ( r1 @ D @ E )
                                      | ( p3 @ E ) )
                                  | ~ ( p2 @ D ) ) )
                      | ~ ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ~ ! [D: $i] :
                                      ( ~ ( r1 @ C @ D )
                                      | ~ ( ! [E: $i] :
                                              ( ~ ( r1 @ D @ E )
                                              | ( p3 @ E ) )
                                          | ~ ( p2 @ D ) ) )
                                & ( p2 @ C )
                                & ~ ! [D: $i] :
                                      ( ~ ( r1 @ C @ D )
                                      | ~ ! [E: $i] :
                                            ( ~ ( r1 @ D @ E )
                                            | ~ ! [F: $i] :
                                                  ( ~ ( r1 @ E @ F )
                                                  | ~ ( p2 @ F ) ) ) ) ) ) ) )
            | ( ~ ( p1 @ A )
              & ~ ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p1 @ C ) ) )
              & ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ( p1 @ B )
                  | ~ ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ~ ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p1 @ D ) )
                            & ( p1 @ C ) ) ) ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ~ ! [D: $i] :
                          ( ~ ( r1 @ C @ D )
                          | ( p1 @ D ) ) )
                | ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ( p1 @ C ) ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ! [C: $i] :
                      ( ~ ( r1 @ B @ C )
                      | ~ ! [D: $i] :
                            ( ~ ( r1 @ C @ D )
                            | ( p2 @ D ) ) ) )
            | ~ ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ! [C: $i] :
                      ( ~ ( r1 @ B @ C )
                      | ! [D: $i] :
                          ( ~ ( r1 @ C @ D )
                          | ~ ( p1 @ D ) ) )
                  | ~ ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( p1 @ C ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ~ ? [A: $i] :
          ~ ( ~ ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( p4 @ B ) )
            | ~ ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ~ ( ~ ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ! [E: $i] :
                                      ( ~ ( r1 @ D @ E )
                                      | ( p3 @ E ) )
                                  | ~ ( p2 @ D ) ) )
                      | ~ ! [C: $i] :
                            ( ~ ( r1 @ B @ C )
                            | ~ ( ~ ! [D: $i] :
                                      ( ~ ( r1 @ C @ D )
                                      | ~ ( ! [E: $i] :
                                              ( ~ ( r1 @ D @ E )
                                              | ( p3 @ E ) )
                                          | ~ ( p2 @ D ) ) )
                                & ( p2 @ C )
                                & ~ ! [D: $i] :
                                      ( ~ ( r1 @ C @ D )
                                      | ~ ! [E: $i] :
                                            ( ~ ( r1 @ D @ E )
                                            | ~ ! [F: $i] :
                                                  ( ~ ( r1 @ E @ F )
                                                  | ~ ( p2 @ F ) ) ) ) ) ) ) )
            | ( ~ ( p1 @ A )
              & ~ ! [B: $i] :
                    ( ~ ( r1 @ A @ B )
                    | ~ ! [C: $i] :
                          ( ~ ( r1 @ B @ C )
                          | ( p1 @ C ) ) )
              & ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ( p1 @ B )
                  | ~ ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( ~ ! [D: $i] :
                                  ( ~ ( r1 @ C @ D )
                                  | ( p1 @ D ) )
                            & ( p1 @ C ) ) ) ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ~ ! [D: $i] :
                          ( ~ ( r1 @ C @ D )
                          | ( p1 @ D ) ) )
                | ! [C: $i] :
                    ( ~ ( r1 @ B @ C )
                    | ( p1 @ C ) ) )
            | ! [B: $i] :
                ( ~ ( r1 @ A @ B )
                | ~ ! [C: $i] :
                      ( ~ ( r1 @ B @ C )
                      | ~ ! [D: $i] :
                            ( ~ ( r1 @ C @ D )
                            | ( p2 @ D ) ) ) )
            | ~ ! [B: $i] :
                  ( ~ ( r1 @ A @ B )
                  | ! [C: $i] :
                      ( ~ ( r1 @ B @ C )
                      | ! [D: $i] :
                          ( ~ ( r1 @ C @ D )
                          | ~ ( p1 @ D ) ) )
                  | ~ ! [C: $i] :
                        ( ~ ( r1 @ B @ C )
                        | ~ ( p1 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i] : ( r1 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

thf(50,plain,
    ! [A: $i] : ( r1 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1 @ A @ B )
        & ( r1 @ B @ C ) )
     => ( r1 @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

thf(52,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1 @ A @ B )
        & ( r1 @ B @ C ) )
     => ( r1 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(31771,plain,
    $false,
    inference(e,[status(thm)],[5,50,52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL688+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n002.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 16:12:05 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.82/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.15/0.97  % [INFO] 	 Parsing done (125ms). 
% 1.15/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.24  % [INFO] 	 Scanning for conjecture ... 
% 2.01/1.33  % [INFO] 	 Found a conjecture and 2 axioms. Running axiom selection ... 
% 2.01/1.36  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.01/1.37  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.01/1.38  % [INFO] 	 Type checking passed. 
% 2.01/1.38  % [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 ... 
% 78.37/13.40  % External prover 'e' found a proof!
% 78.37/13.40  % [INFO] 	 Killing All external provers ... 
% 78.37/13.41  % Time passed: 12892ms (effective reasoning time: 12425ms)
% 78.37/13.41  % 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)>
% 78.37/13.41  % Axioms used in derivation (2): reflexivity, transitivity
% 78.37/13.41  % No. of inferences in proof: 8
% 78.37/13.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12892 ms resp. 12425 ms w/o parsing
% 78.37/13.43  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 78.37/13.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------