TSTP Solution File: SYO605+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SYO605+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 12:36:41 EDT 2023

% Result   : Theorem 15.87s 3.48s
% Output   : Refutation 15.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   17 (   1 unt;   5 typ;   0 def)
%            Number of atoms       :  205 (   0 equ;   0 cnn)
%            Maximal formula atoms :   57 (  17 avg)
%            Number of connectives :  624 (  23   ~;  91   |;  93   &; 408   @)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   73 (   0   ^;  31   !;  42   ?;  73   :)

% Comments : 
%------------------------------------------------------------------------------
thf(g_true_only_type,type,
    g_true_only: $i > $i > $o ).

thf(g_both_type,type,
    g_both: $i > $i > $o ).

thf(g_false_only_type,type,
    g_false_only: $i > $i > $o ).

thf(g_true_type,type,
    g_true: $i > $i > $o ).

thf(g_false_type,type,
    g_false: $i > $i > $o ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( g_true_only @ A @ B )
      | ( g_both @ A @ B )
      | ( g_false_only @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exhaustion_g) ).

thf(101,plain,
    ! [A: $i,B: $i] :
      ( ( g_true_only @ A @ B )
      | ( g_both @ A @ B )
      | ( g_false_only @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( g_both @ A @ B )
    <=> ( ( g_true @ A @ B )
        & ( g_false @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both_g) ).

thf(89,plain,
    ! [A: $i,B: $i] :
      ( ( ( g_both @ A @ B )
       => ( ( g_true @ A @ B )
          & ( g_false @ A @ B ) ) )
      & ( ( ( g_true @ A @ B )
          & ( g_false @ A @ B ) )
       => ( g_both @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,conjecture,
    ( ! [A: $i] :
      ? [B: $i] :
        ( ( ( g_true_only @ B @ A )
          & ( ( g_both @ B @ B )
            | ( g_false_only @ B @ B ) ) )
        | ( ( g_both @ B @ A )
          & ( ( g_true_only @ B @ B )
            | ( g_false_only @ B @ B ) ) )
        | ( ( g_false_only @ B @ A )
          & ( ( g_true_only @ B @ B )
            | ( g_both @ B @ B ) ) ) )
    | ? [A: $i] :
      ! [B: $i] :
      ? [C: $i] :
        ( ( ( g_true_only @ C @ B )
          & ( ( g_both @ C @ A )
            | ( g_true_only @ C @ A ) ) )
        | ( ( g_both @ C @ B )
          & ( ( g_false_only @ C @ A )
            | ( g_true_only @ C @ A ) ) )
        | ( ( g_false_only @ C @ B )
          & ( ( g_false_only @ C @ A )
            | ( g_both @ C @ A ) ) ) )
    | ( ? [A: $i] :
          ( ? [B: $i] :
              ( ( g_both @ B @ A )
              & ( g_both @ B @ B ) )
          & ~ ? [B: $i] :
                ( ( ( g_true_only @ B @ A )
                  & ( ( g_both @ B @ B )
                    | ( g_false_only @ B @ B ) ) )
                | ( ( g_both @ B @ A )
                  & ( ( g_true_only @ B @ B )
                    | ( g_false_only @ B @ B ) ) )
                | ( ( g_false_only @ B @ A )
                  & ( ( g_true_only @ B @ B )
                    | ( g_both @ B @ B ) ) ) ) )
      & ~ ? [A: $i] :
          ! [B: $i] :
            ( ( ( g_true_only @ B @ A )
              & ( g_true_only @ B @ B ) )
            | ( ( g_false_only @ B @ A )
              & ( g_false_only @ B @ B ) ) )
      & ? [A: $i] :
          ( ? [B: $i] :
              ( ? [C: $i] :
                  ( ( g_both @ C @ B )
                  & ( g_both @ C @ A ) )
              & ~ ? [C: $i] :
                    ( ( ( g_true_only @ C @ B )
                      & ( ( g_both @ C @ A )
                        | ( g_true_only @ C @ A ) ) )
                    | ( ( g_both @ C @ B )
                      & ( ( g_false_only @ C @ A )
                        | ( g_true_only @ C @ A ) ) )
                    | ( ( g_false_only @ C @ B )
                      & ( ( g_false_only @ C @ A )
                        | ( g_both @ C @ A ) ) ) ) )
          & ~ ? [B: $i] :
              ! [C: $i] :
                ( ( ( g_true_only @ C @ B )
                  & ( g_false_only @ C @ A ) )
                | ( ( g_false_only @ C @ B )
                  & ( g_true_only @ C @ A ) ) ) )
      & ~ ? [A: $i] :
          ! [B: $i] :
          ? [C: $i] :
            ( ( ( g_true_only @ C @ B )
              & ( ( g_both @ C @ A )
                | ( g_true_only @ C @ A ) ) )
            | ( ( g_both @ C @ B )
              & ( ( g_false_only @ C @ A )
                | ( g_true_only @ C @ A ) ) )
            | ( ( g_false_only @ C @ B )
              & ( ( g_false_only @ C @ A )
                | ( g_both @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc4) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
        ? [B: $i] :
          ( ( ( g_true_only @ B @ A )
            & ( ( g_both @ B @ B )
              | ( g_false_only @ B @ B ) ) )
          | ( ( g_both @ B @ A )
            & ( ( g_true_only @ B @ B )
              | ( g_false_only @ B @ B ) ) )
          | ( ( g_false_only @ B @ A )
            & ( ( g_true_only @ B @ B )
              | ( g_both @ B @ B ) ) ) )
      | ? [A: $i] :
        ! [B: $i] :
        ? [C: $i] :
          ( ( ( g_true_only @ C @ B )
            & ( ( g_both @ C @ A )
              | ( g_true_only @ C @ A ) ) )
          | ( ( g_both @ C @ B )
            & ( ( g_false_only @ C @ A )
              | ( g_true_only @ C @ A ) ) )
          | ( ( g_false_only @ C @ B )
            & ( ( g_false_only @ C @ A )
              | ( g_both @ C @ A ) ) ) )
      | ( ? [A: $i] :
            ( ? [B: $i] :
                ( ( g_both @ B @ A )
                & ( g_both @ B @ B ) )
            & ~ ? [B: $i] :
                  ( ( ( g_true_only @ B @ A )
                    & ( ( g_both @ B @ B )
                      | ( g_false_only @ B @ B ) ) )
                  | ( ( g_both @ B @ A )
                    & ( ( g_true_only @ B @ B )
                      | ( g_false_only @ B @ B ) ) )
                  | ( ( g_false_only @ B @ A )
                    & ( ( g_true_only @ B @ B )
                      | ( g_both @ B @ B ) ) ) ) )
        & ~ ? [A: $i] :
            ! [B: $i] :
              ( ( ( g_true_only @ B @ A )
                & ( g_true_only @ B @ B ) )
              | ( ( g_false_only @ B @ A )
                & ( g_false_only @ B @ B ) ) )
        & ? [A: $i] :
            ( ? [B: $i] :
                ( ? [C: $i] :
                    ( ( g_both @ C @ B )
                    & ( g_both @ C @ A ) )
                & ~ ? [C: $i] :
                      ( ( ( g_true_only @ C @ B )
                        & ( ( g_both @ C @ A )
                          | ( g_true_only @ C @ A ) ) )
                      | ( ( g_both @ C @ B )
                        & ( ( g_false_only @ C @ A )
                          | ( g_true_only @ C @ A ) ) )
                      | ( ( g_false_only @ C @ B )
                        & ( ( g_false_only @ C @ A )
                          | ( g_both @ C @ A ) ) ) ) )
            & ~ ? [B: $i] :
                ! [C: $i] :
                  ( ( ( g_true_only @ C @ B )
                    & ( g_false_only @ C @ A ) )
                  | ( ( g_false_only @ C @ B )
                    & ( g_true_only @ C @ A ) ) ) )
        & ~ ? [A: $i] :
            ! [B: $i] :
            ? [C: $i] :
              ( ( ( g_true_only @ C @ B )
                & ( ( g_both @ C @ A )
                  | ( g_true_only @ C @ A ) ) )
              | ( ( g_both @ C @ B )
                & ( ( g_false_only @ C @ A )
                  | ( g_true_only @ C @ A ) ) )
              | ( ( g_false_only @ C @ B )
                & ( ( g_false_only @ C @ A )
                  | ( g_both @ C @ A ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ( ! [A: $i] :
        ? [B: $i] :
          ( ( ( g_true_only @ B @ A )
            & ( ( g_both @ B @ B )
              | ( g_false_only @ B @ B ) ) )
          | ( ( g_both @ B @ A )
            & ( ( g_true_only @ B @ B )
              | ( g_false_only @ B @ B ) ) )
          | ( ( g_false_only @ B @ A )
            & ( ( g_true_only @ B @ B )
              | ( g_both @ B @ B ) ) ) )
      | ? [A: $i] :
        ! [B: $i] :
        ? [C: $i] :
          ( ( ( g_true_only @ C @ B )
            & ( ( g_both @ C @ A )
              | ( g_true_only @ C @ A ) ) )
          | ( ( g_both @ C @ B )
            & ( ( g_false_only @ C @ A )
              | ( g_true_only @ C @ A ) ) )
          | ( ( g_false_only @ C @ B )
            & ( ( g_false_only @ C @ A )
              | ( g_both @ C @ A ) ) ) )
      | ( ? [A: $i] :
            ( ? [B: $i] :
                ( ( g_both @ B @ A )
                & ( g_both @ B @ B ) )
            & ~ ? [B: $i] :
                  ( ( ( g_true_only @ B @ A )
                    & ( ( g_both @ B @ B )
                      | ( g_false_only @ B @ B ) ) )
                  | ( ( g_both @ B @ A )
                    & ( ( g_true_only @ B @ B )
                      | ( g_false_only @ B @ B ) ) )
                  | ( ( g_false_only @ B @ A )
                    & ( ( g_true_only @ B @ B )
                      | ( g_both @ B @ B ) ) ) ) )
        & ~ ? [A: $i] :
            ! [B: $i] :
              ( ( ( g_true_only @ B @ A )
                & ( g_true_only @ B @ B ) )
              | ( ( g_false_only @ B @ A )
                & ( g_false_only @ B @ B ) ) )
        & ? [A: $i] :
            ( ? [B: $i] :
                ( ? [C: $i] :
                    ( ( g_both @ C @ B )
                    & ( g_both @ C @ A ) )
                & ~ ? [C: $i] :
                      ( ( ( g_true_only @ C @ B )
                        & ( ( g_both @ C @ A )
                          | ( g_true_only @ C @ A ) ) )
                      | ( ( g_both @ C @ B )
                        & ( ( g_false_only @ C @ A )
                          | ( g_true_only @ C @ A ) ) )
                      | ( ( g_false_only @ C @ B )
                        & ( ( g_false_only @ C @ A )
                          | ( g_both @ C @ A ) ) ) ) )
            & ~ ? [B: $i] :
                ! [C: $i] :
                  ( ( ( g_true_only @ C @ B )
                    & ( g_false_only @ C @ A ) )
                  | ( ( g_false_only @ C @ B )
                    & ( g_true_only @ C @ A ) ) ) )
        & ~ ? [A: $i] :
            ! [B: $i] :
            ? [C: $i] :
              ( ( ( g_true_only @ C @ B )
                & ( ( g_both @ C @ A )
                  | ( g_true_only @ C @ A ) ) )
              | ( ( g_both @ C @ B )
                & ( ( g_false_only @ C @ A )
                  | ( g_true_only @ C @ A ) ) )
              | ( ( g_false_only @ C @ B )
                & ( ( g_false_only @ C @ A )
                  | ( g_both @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( g_false_only @ A @ B )
    <=> ( ( g_false @ A @ B )
        & ~ ( g_true @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_only_g) ).

thf(95,plain,
    ! [A: $i,B: $i] :
      ( ( ( g_false_only @ A @ B )
       => ( ( g_false @ A @ B )
          & ~ ( g_true @ A @ B ) ) )
      & ( ( ( g_false @ A @ B )
          & ~ ( g_true @ A @ B ) )
       => ( g_false_only @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( g_true_only @ A @ B )
    <=> ( ( g_true @ A @ B )
        & ~ ( g_false @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_only_g) ).

thf(83,plain,
    ! [A: $i,B: $i] :
      ( ( ( g_true_only @ A @ B )
       => ( ( g_true @ A @ B )
          & ~ ( g_false @ A @ B ) ) )
      & ( ( ( g_true @ A @ B )
          & ~ ( g_false @ A @ B ) )
       => ( g_true_only @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(2558,plain,
    $false,
    inference(e,[status(thm)],[101,89,7,95,83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO605+1 : TPTP v8.1.2. Released v7.0.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n021.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 18:16:28 EDT 2023
% 0.22/0.36  % CPUTime  : 
% 0.85/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.95  % [INFO] 	 Parsing done (123ms). 
% 1.23/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.14  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.15  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.22  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 2.02/1.25  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.02/1.25  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.02/1.26  % [INFO] 	 Type checking passed. 
% 2.02/1.26  % [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 ... 
% 15.87/3.48  % External prover 'e' found a proof!
% 15.87/3.48  % [INFO] 	 Killing All external provers ... 
% 15.87/3.48  % Time passed: 2990ms (effective reasoning time: 2523ms)
% 15.87/3.48  % 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)>
% 15.87/3.48  % Axioms used in derivation (4): exhaustion_g, both_g, false_only_g, true_only_g
% 15.87/3.48  % No. of inferences in proof: 12
% 15.87/3.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2990 ms resp. 2523 ms w/o parsing
% 15.87/3.51  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.87/3.51  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------