TSTP Solution File: SWV409+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : Fri May 19 12:15:39 EDT 2023

% Result   : Theorem 3.41s 1.97s
% Output   : Refutation 3.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   58 (  19 unt;  12 typ;   0 def)
%            Number of atoms       :  116 (  27 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  449 (  15   ~;  11   |;  31   &; 364   @)
%                                         (   3 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :  130 (   0   ^; 123   !;   7   ?; 130   :)

% Comments : 
%------------------------------------------------------------------------------
thf(contains_slb_type,type,
    contains_slb: $i > $i > $o ).

thf(strictly_less_than_type,type,
    strictly_less_than: $i > $i > $o ).

thf(pair_in_list_type,type,
    pair_in_list: $i > $i > $i > $o ).

thf(update_slb_type,type,
    update_slb: $i > $i > $i ).

thf(less_than_type,type,
    less_than: $i > $i > $o ).

thf(isnonempty_slb_type,type,
    isnonempty_slb: $i > $o ).

thf(insert_slb_type,type,
    insert_slb: $i > $i > $i ).

thf(pair_type,type,
    pair: $i > $i > $i ).

thf(lookup_slb_type,type,
    lookup_slb: $i > $i > $i ).

thf(remove_slb_type,type,
    remove_slb: $i > $i > $i ).

thf(create_slb_type,type,
    create_slb: $i ).

thf(bottom_type,type,
    bottom: $i ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
    <=> ( ( pair_in_list @ A @ C @ E )
        | ( ( B = C )
          & ( D = E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

thf(85,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
       => ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) ) )
      & ( ( ( pair_in_list @ A @ C @ E )
          | ( ( B = C )
            & ( D = E ) ) )
       => ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

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

thf(70,plain,
    ! [A: $i,B: $i] :
      ( ( ( strictly_less_than @ A @ B )
       => ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) ) )
      & ( ( ( less_than @ A @ B )
          & ~ ( less_than @ B @ A ) )
       => ( strictly_less_than @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( contains_slb @ A @ B )
     => ? [C: $i] : ( pair_in_list @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).

thf(65,plain,
    ! [A: $i,B: $i] :
      ( ( contains_slb @ A @ B )
     => ? [C: $i] : ( pair_in_list @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( less_than @ A @ B )
        & ( less_than @ B @ C ) )
     => ( less_than @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

thf(53,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( less_than @ A @ B )
        & ( less_than @ B @ C ) )
     => ( less_than @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( less_than @ C @ D )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).

thf(96,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( less_than @ C @ D )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

thf(34,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ~ ( pair_in_list @ create_slb @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

thf(80,plain,
    ! [A: $i,B: $i] :
      ~ ( pair_in_list @ create_slb @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(8,axiom,
    ! [A: $i] : ( less_than @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

thf(48,plain,
    ! [A: $i] : ( less_than @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( lookup_slb @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).

thf(99,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( lookup_slb @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( strictly_less_than @ D @ C )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).

thf(55,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( strictly_less_than @ D @ C )
     => ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

thf(58,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B != C )
        & ( contains_slb @ A @ C ) )
     => ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
        = ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( pair_in_list @ A @ B @ C )
        & ( strictly_less_than @ B @ D )
        & ( less_than @ D @ C ) )
     => ? [E: $i] :
          ( ( pair_in_list @ ( update_slb @ A @ D ) @ B @ E )
          & ( less_than @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l49) ).

thf(62,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( pair_in_list @ A @ B @ C )
        & ( strictly_less_than @ B @ D )
        & ( less_than @ D @ C ) )
     => ? [E: $i] :
          ( ( pair_in_list @ ( update_slb @ A @ D ) @ B @ E )
          & ( less_than @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( less_than @ A @ B )
      | ( less_than @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).

thf(83,plain,
    ! [A: $i,B: $i] :
      ( ( less_than @ A @ B )
      | ( less_than @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( contains_slb @ A @ B )
        & ( strictly_less_than @ B @ C ) )
     => ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ C )
        | ? [D: $i] :
            ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ D )
            & ( less_than @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_co) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( contains_slb @ A @ B )
          & ( strictly_less_than @ B @ C ) )
       => ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ C )
          | ? [D: $i] :
              ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ D )
              & ( less_than @ C @ D ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(24,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( contains_slb @ A @ B )
          & ( strictly_less_than @ B @ C ) )
       => ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ C )
          | ? [D: $i] :
              ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ D )
              & ( less_than @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ~ ( isnonempty_slb @ create_slb ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).

thf(37,plain,
    ~ ( isnonempty_slb @ create_slb ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(18,axiom,
    ! [A: $i] : ( less_than @ bottom @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).

thf(78,plain,
    ! [A: $i] : ( less_than @ bottom @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).

thf(29,plain,
    ! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( pair_in_list @ A @ B @ C )
        & ( strictly_less_than @ B @ D )
        & ( strictly_less_than @ C @ D ) )
     => ( pair_in_list @ ( update_slb @ A @ D ) @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l48) ).

thf(76,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( pair_in_list @ A @ B @ C )
        & ( strictly_less_than @ B @ D )
        & ( strictly_less_than @ C @ D ) )
     => ( pair_in_list @ ( update_slb @ A @ D ) @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
    <=> ( ( contains_slb @ A @ C )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

thf(39,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
       => ( ( contains_slb @ A @ C )
          | ( B = C ) ) )
      & ( ( ( contains_slb @ A @ C )
          | ( B = C ) )
       => ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(9,axiom,
    ! [A: $i] :
      ~ ( contains_slb @ create_slb @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).

thf(50,plain,
    ! [A: $i] :
      ~ ( contains_slb @ create_slb @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( update_slb @ create_slb @ A )
      = create_slb ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

thf(67,plain,
    ! [A: $i] :
      ( ( update_slb @ create_slb @ A )
      = create_slb ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

thf(31,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(103,plain,
    $false,
    inference(e,[status(thm)],[85,70,65,53,96,34,80,48,99,55,58,62,83,24,37,78,29,76,39,50,67,31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10  % Command  : run_Leo-III %s %d
% 0.10/0.29  % Computer : n012.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 300
% 0.10/0.29  % DateTime : Fri May 19 02:09:18 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.72/0.77  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.09/0.91  % [INFO] 	 Parsing done (145ms). 
% 1.16/0.93  % [INFO] 	 Running in sequential loop mode. 
% 1.47/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.47/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.64/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.26  % [INFO] 	 Found a conjecture and 21 axioms. Running axiom selection ... 
% 1.92/1.31  % [INFO] 	 Axiom selection finished. Selected 21 axioms (removed 0 axioms). 
% 1.92/1.35  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.92/1.36  % [INFO] 	 Type checking passed. 
% 1.92/1.37  % [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 ... 
% 3.41/1.97  % External prover 'e' found a proof!
% 3.41/1.97  % [INFO] 	 Killing All external provers ... 
% 3.41/1.97  % Time passed: 1547ms (effective reasoning time: 1035ms)
% 3.41/1.97  % 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)>
% 3.41/1.97  % Axioms used in derivation (21): ax20, ax24, stricly_smaller_definition, ax28, ax27, ax21, l45_l49, l45_li4647, ax22, ax19, totality, ax23, ax25, reflexivity, l45_l48, ax26, bottom_smallest, transitivity, ax30, ax18, ax29
% 3.41/1.97  % No. of inferences in proof: 46
% 3.41/1.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1547 ms resp. 1035 ms w/o parsing
% 3.79/2.02  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.79/2.02  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------