TSTP Solution File: SEV292^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEV292^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 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 : Tue May 21 04:10:18 EDT 2024

% Result   : Theorem 58.93s 15.60s
% Output   : Refutation 58.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   40 (   5 unt;   8 typ;   4 def)
%            Number of atoms       :  158 (  61 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  508 ( 120   ~;  42   |; 106   &; 231   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  150 ( 150   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :  165 (  63   ^  30   !;  72   ?; 165   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cP_type,type,
    cP: ( ( $i > $o ) > $o ) > $o ).

thf(cONE_type,type,
    cONE: ( $i > $o ) > $o ).

thf(cONE_def,definition,
    ( cONE
    = ( cSUCC @ cZERO ) ) ).

thf(cSUCC_type,type,
    cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).

thf(cSUCC_def,definition,
    ( cSUCC
    = ( ^ [A: ( $i > $o ) > $o,B: $i > $o] :
        ? [C: $i] :
          ( ( B @ C )
          & ( A
            @ ^ [D: $i] :
                ( ( D != C )
                & ( B @ D ) ) ) ) ) ) ).

thf(cZERO_type,type,
    cZERO: ( $i > $o ) > $o ).

thf(cZERO_def,definition,
    ( cZERO
    = ( ^ [A: $i > $o] :
          ~ ? [B: $i] : ( A @ B ) ) ) ).

thf(c_less__eq__type,type,
    c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(c_less__eq__def,definition,
    ( c_less__eq_
    = ( ^ [A: ( $i > $o ) > $o,B: ( $i > $o ) > $o] :
        ! [C: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( C @ A )
            & ! [D: ( $i > $o ) > $o] :
                ( ( C @ D )
               => ( C @ ( cSUCC @ D ) ) ) )
         => ( C @ B ) ) ) ) ).

thf(sk1_type,type,
    sk1: ( ( $i > $o ) > $o ) > $o ).

thf(sk2_type,type,
    sk2: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(sk3_type,type,
    sk3: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(1,conjecture,
    ( ( cP @ cONE )
   => ? [A: ( $i > $o ) > $o] :
        ( ( c_less__eq_ @ cZERO @ A )
        & ( c_less__eq_ @ A @ ( cSUCC @ cONE ) )
        & ( cP @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE7A) ).

thf(2,negated_conjecture,
    ~ ( ( cP @ cONE )
     => ? [A: ( $i > $o ) > $o] :
          ( ( c_less__eq_ @ cZERO @ A )
          & ( c_less__eq_ @ A @ ( cSUCC @ cONE ) )
          & ( cP @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( cP
        @ ^ [A: $i > $o] :
          ? [B: $i] :
            ( ( A @ B )
            & ~ ? [C: $i] :
                  ( ( C != B )
                  & ( A @ C ) ) ) )
     => ? [A: ( $i > $o ) > $o] :
          ( ! [B: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( B
                  @ ^ [C: $i > $o] :
                      ~ ? [D: $i] : ( C @ D ) )
                & ! [C: ( $i > $o ) > $o] :
                    ( ( B @ C )
                   => ( B
                      @ ^ [D: $i > $o] :
                        ? [E: $i] :
                          ( ( D @ E )
                          & ( C
                            @ ^ [F: $i] :
                                ( ( F != E )
                                & ( D @ F ) ) ) ) ) ) )
             => ( B @ A ) )
          & ! [B: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( B @ A )
                & ! [C: ( $i > $o ) > $o] :
                    ( ( B @ C )
                   => ( B
                      @ ^ [D: $i > $o] :
                        ? [E: $i] :
                          ( ( D @ E )
                          & ( C
                            @ ^ [F: $i] :
                                ( ( F != E )
                                & ( D @ F ) ) ) ) ) ) )
             => ( B
                @ ^ [C: $i > $o] :
                  ? [D: $i] :
                    ( ( C @ D )
                    & ? [E: $i] :
                        ( ( E != D )
                        & ( C @ E )
                        & ~ ? [F: $i] :
                              ( ( F != E )
                              & ( F != D )
                              & ( C @ F ) ) ) ) ) )
          & ( cP @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ( sk3 @ A @ A )
      | ~ ( cP @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ~ ( sk3 @ A @ B )
      | ( sk3 @ A
        @ ^ [C: $i > $o] :
          ? [D: $i] :
            ( ( C @ D )
            & ( B
              @ ^ [E: $i] :
                  ( ( E != D )
                  & ( C @ E ) ) ) ) )
      | ~ ( cP @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ~ ( sk3 @ A @ B )
      | ( sk3 @ A
        @ ^ [C: $i > $o] :
          ? [D: $i] :
            ( ( C @ D )
            & ( B
              @ ^ [E: $i] :
                  ( ( E != D )
                  & ( C @ E ) ) ) ) )
      | ~ ( cP @ A ) ),
    inference(simp,[status(thm)],[4]) ).

thf(157,plain,
    ! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ~ ( cP @ A )
      | ( sk1 @ B )
      | ( sk3 @ B
        @ ^ [D: $i > $o] :
          ? [E: $i] :
            ( ( D @ E )
            & ( C
              @ ^ [F: $i] :
                  ( ( F != E )
                  & ( D @ F ) ) ) ) )
      | ~ ( cP @ B )
      | ( ( sk3 @ A @ A )
       != ( sk3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[5,11]) ).

thf(158,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ~ ( cP @ A )
      | ( sk1 @ A )
      | ( sk3 @ A
        @ ^ [B: $i > $o] :
          ? [C: $i] :
            ( ( B @ C )
            & ( A
              @ ^ [D: $i] :
                  ( ( D != C )
                  & ( B @ D ) ) ) ) )
      | ~ ( cP @ A ) ),
    inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(199,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ~ ( cP @ A )
      | ( sk3 @ A
        @ ^ [B: $i > $o] :
          ? [C: $i] :
            ( ( B @ C )
            & ( A
              @ ^ [D: $i] :
                  ( ( D != C )
                  & ( B @ D ) ) ) ) ) ),
    inference(simp,[status(thm)],[158]) ).

thf(9,plain,
    ( cP
    @ ^ [A: $i > $o] :
      ? [B: $i] :
        ( ( A @ B )
        & ~ ? [C: $i] :
              ( ( C != B )
              & ( A @ C ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ~ ( sk3 @ A
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ? [D: $i] :
                  ( ( D != C )
                  & ( B @ D )
                  & ~ ? [E: $i] :
                        ( ( E != D )
                        & ( E != C )
                        & ( B @ E ) ) ) ) )
      | ~ ( cP @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(65,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ~ ( sk3 @ A
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ? [D: $i] :
                  ( ( D != C )
                  & ( B @ D )
                  & ~ ? [E: $i] :
                        ( ( E != D )
                        & ( E != C )
                        & ( B @ E ) ) ) ) )
      | ( ( cP
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ~ ? [D: $i] :
                    ( ( D != C )
                    & ( B @ D ) ) ) )
       != ( cP @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9,7]) ).

thf(66,plain,
    ( ( sk1
      @ ^ [A: $i > $o] :
        ? [B: $i] :
          ( ( A @ B )
          & ~ ? [C: $i] :
                ( ( C != B )
                & ( A @ C ) ) ) )
    | ~ ( sk3
        @ ^ [A: $i > $o] :
          ? [B: $i] :
            ( ( A @ B )
            & ~ ? [C: $i] :
                  ( ( C != B )
                  & ( A @ C ) ) )
        @ ^ [A: $i > $o] :
          ? [B: $i] :
            ( ( A @ B )
            & ? [C: $i] :
                ( ( C != B )
                & ( A @ C )
                & ~ ? [D: $i] :
                      ( ( D != C )
                      & ( D != B )
                      & ( A @ D ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( ^ [B: $i > $o] : ? [C: $i] : ( ( B @ C ) & ~ ( ? [D: $i] : ( ( D != C ) & ( B @ D ) ) ) ) ))]]) ).

thf(8,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ( sk2 @ A
        @ ^ [B: $i > $o] :
            ~ ? [C: $i] : ( B @ C ) )
      | ~ ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
      ( ~ ( sk2 @ A @ B )
      | ( sk2 @ A
        @ ^ [C: $i > $o] :
          ? [D: $i] :
            ( ( C @ D )
            & ( B
              @ ^ [E: $i] :
                  ( ( E != D )
                  & ( C @ E ) ) ) ) )
      | ~ ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ~ ( sk2 @ A @ A )
      | ~ ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(15,plain,
    ! [C: ( $i > $o ) > $o,B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
      ( ~ ( sk2 @ A @ B )
      | ~ ( sk1 @ A )
      | ~ ( sk1 @ C )
      | ( ( sk2 @ A
          @ ^ [D: $i > $o] :
            ? [E: $i] :
              ( ( D @ E )
              & ( B
                @ ^ [F: $i] :
                    ( ( F != E )
                    & ( D @ F ) ) ) ) )
       != ( sk2 @ C @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[6,10]) ).

thf(19,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ~ ( sk2
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ( A
                @ ^ [D: $i] :
                    ( ( D != C )
                    & ( B @ D ) ) ) )
          @ A )
      | ~ ( sk1
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ( A
                @ ^ [D: $i] :
                    ( ( D != C )
                    & ( B @ D ) ) ) ) )
      | ~ ( sk1
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ( A
                @ ^ [D: $i] :
                    ( ( D != C )
                    & ( B @ D ) ) ) ) ) ),
    inference(pre_uni,[status(thm)],[15:[bind(A,$thf( ^ [D: $i > $o] : ? [E: $i] : ( ( D @ E ) & ( B @ ^ [F: $i] : ( ( F != E ) & ( D @ F ) ) ) ) )),bind(B,$thf( B )),bind(C,$thf( ^ [D: $i > $o] : ? [E: $i] : ( ( D @ E ) & ( B @ ^ [F: $i] : ( ( F != E ) & ( D @ F ) ) ) ) ))]]) ).

thf(22,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ~ ( sk2
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ( A
                @ ^ [D: $i] :
                    ( ( D != C )
                    & ( B @ D ) ) ) )
          @ A )
      | ~ ( sk1
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ( A
                @ ^ [D: $i] :
                    ( ( D != C )
                    & ( B @ D ) ) ) ) ) ),
    inference(simp,[status(thm)],[19]) ).

thf(25,plain,
    ! [B: ( $i > $o ) > $o,A: ( $i > $o ) > $o] :
      ( ~ ( sk1 @ A )
      | ~ ( sk1
          @ ^ [C: $i > $o] :
            ? [D: $i] :
              ( ( C @ D )
              & ( B
                @ ^ [E: $i] :
                    ( ( E != D )
                    & ( C @ E ) ) ) ) )
      | ( ( sk2 @ A
          @ ^ [C: $i > $o] :
              ~ ? [D: $i] : ( C @ D ) )
       != ( sk2
          @ ^ [C: $i > $o] :
            ? [D: $i] :
              ( ( C @ D )
              & ( B
                @ ^ [E: $i] :
                    ( ( E != D )
                    & ( C @ E ) ) ) )
          @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8,22]) ).

thf(27,plain,
    ( ~ ( sk1
        @ ^ [A: $i > $o] :
          ? [B: $i] :
            ( ( A @ B )
            & ~ ? [C: $i] :
                  ( ( C != B )
                  & ( A @ C ) ) ) )
    | ~ ( sk1
        @ ^ [A: $i > $o] :
          ? [B: $i] :
            ( ( A @ B )
            & ~ ? [C: $i] :
                  ( ( C != B )
                  & ( A @ C ) ) ) ) ),
    inference(pre_uni,[status(thm)],[25:[bind(A,$thf( ^ [C: $i > $o] : ? [D: $i] : ( ( C @ D ) & ~ ( ? [E: $i] : ( ( E != D ) & ( C @ E ) ) ) ) )),bind(B,$thf( ^ [C: $i > $o] : ~ ( ? [D: $i] : ( C @ D ) ) ))]]) ).

thf(29,plain,
    ~ ( sk1
      @ ^ [A: $i > $o] :
        ? [B: $i] :
          ( ( A @ B )
          & ~ ? [C: $i] :
                ( ( C != B )
                & ( A @ C ) ) ) ),
    inference(simp,[status(thm)],[27]) ).

thf(206,plain,
    ( $false
    | ~ ( sk3
        @ ^ [A: $i > $o] :
          ? [B: $i] :
            ( ( A @ B )
            & ~ ? [C: $i] :
                  ( ( C != B )
                  & ( A @ C ) ) )
        @ ^ [A: $i > $o] :
          ? [B: $i] :
            ( ( A @ B )
            & ? [C: $i] :
                ( ( C != B )
                & ( A @ C )
                & ~ ? [D: $i] :
                      ( ( D != C )
                      & ( D != B )
                      & ( A @ D ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[66,29]) ).

thf(207,plain,
    ~ ( sk3
      @ ^ [A: $i > $o] :
        ? [B: $i] :
          ( ( A @ B )
          & ~ ? [C: $i] :
                ( ( C != B )
                & ( A @ C ) ) )
      @ ^ [A: $i > $o] :
        ? [B: $i] :
          ( ( A @ B )
          & ? [C: $i] :
              ( ( C != B )
              & ( A @ C )
              & ~ ? [D: $i] :
                    ( ( D != C )
                    & ( D != B )
                    & ( A @ D ) ) ) ) ),
    inference(simp,[status(thm)],[206]) ).

thf(246,plain,
    ! [A: ( $i > $o ) > $o] :
      ( ( sk1 @ A )
      | ~ ( cP @ A )
      | ( ( sk3 @ A
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ( A
                @ ^ [D: $i] :
                    ( ( D != C )
                    & ( B @ D ) ) ) ) )
       != ( sk3
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ~ ? [D: $i] :
                    ( ( D != C )
                    & ( B @ D ) ) )
          @ ^ [B: $i > $o] :
            ? [C: $i] :
              ( ( B @ C )
              & ? [D: $i] :
                  ( ( D != C )
                  & ( B @ D )
                  & ~ ? [E: $i] :
                        ( ( E != D )
                        & ( E != C )
                        & ( B @ E ) ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[199,207]) ).

thf(250,plain,
    ( ( sk1
      @ ^ [A: $i > $o] :
        ? [B: $i] :
          ( ( A @ B )
          & ~ ? [C: $i] :
                ( ( C != B )
                & ( A @ C ) ) ) )
    | ~ ( cP
        @ ^ [A: $i > $o] :
          ? [B: $i] :
            ( ( A @ B )
            & ~ ? [C: $i] :
                  ( ( C != B )
                  & ( A @ C ) ) ) ) ),
    inference(pre_uni,[status(thm)],[246:[bind(A,$thf( ^ [B: $i > $o] : ? [C: $i] : ( ( B @ C ) & ~ ( ? [D: $i] : ( ( D != C ) & ( B @ D ) ) ) ) ))]]) ).

thf(254,plain,
    ( $false
    | ~ $true ),
    inference(rewrite,[status(thm)],[250,9,29]) ).

thf(255,plain,
    $false,
    inference(simp,[status(thm)],[254]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : SEV292^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.04/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n002.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Sun May 19 18:45:54 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.92/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.31/1.09  % [INFO] 	 Parsing done (160ms). 
% 1.31/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.44  % [INFO] 	 eprover registered as external prover. 
% 1.85/1.45  % [INFO] 	 cvc4 registered as external prover. 
% 1.85/1.45  % [INFO] 	 Scanning for conjecture ... 
% 2.08/1.56  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.08/1.59  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.08/1.59  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.08/1.60  % [INFO] 	 Type checking passed. 
% 2.08/1.60  % [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 ... 
% 58.93/15.60  % [INFO] 	 Killing All external provers ... 
% 58.93/15.60  % Time passed: 15141ms (effective reasoning time: 14497ms)
% 58.93/15.60  % 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)>
% 58.93/15.60  % Axioms used in derivation (0): 
% 58.93/15.60  % No. of inferences in proof: 28
% 58.93/15.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15141 ms resp. 14497 ms w/o parsing
% 58.93/15.66  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 58.93/15.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------