TSTP Solution File: SEU151+1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : SEU151+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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  7 08:08:57 EDT 2024

% Result   : Theorem 3.34s 1.76s
% Output   : Refutation 3.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   14 (   5 unt;   2 typ;   0 def)
%            Number of atoms       :   36 (  24 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :   81 (  13   ~;   5   |;   9   &;  44   @)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   2 con; 0-2 aty)
%            Number of variables   :   29 (   0   ^  29   !;   0   ?;  29   :)

% Comments : 
%------------------------------------------------------------------------------
thf(unordered_pair_type,type,
    unordered_pair: $i > $i > $i ).

thf(in_type,type,
    in: $i > $i > $o ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(17,plain,
    ! [A: $i,B: $i] :
      ( ( unordered_pair @ A @ B )
      = ( unordered_pair @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( ( unordered_pair @ A @ B )
          = ( unordered_pair @ C @ D ) )
        & ( A != C )
        & ( A != D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ~ ( ( ( unordered_pair @ A @ B )
            = ( unordered_pair @ C @ D ) )
          & ( A != C )
          & ( A != D ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ~ ( ( ( unordered_pair @ A @ B )
            = ( unordered_pair @ C @ D ) )
          & ( A != C )
          & ( A != D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(15,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( unordered_pair @ A @ B ) )
    <=> ! [D: $i] :
          ( ( in @ D @ C )
        <=> ( ( D = A )
            | ( D = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

thf(20,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( unordered_pair @ A @ B ) )
       => ! [D: $i] :
            ( ( ( in @ D @ C )
             => ( ( D = A )
                | ( D = B ) ) )
            & ( ( ( D = A )
                | ( D = B ) )
             => ( in @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( in @ D @ C )
             => ( ( D = A )
                | ( D = B ) ) )
            & ( ( ( D = A )
                | ( D = B ) )
             => ( in @ D @ C ) ) )
       => ( C
          = ( unordered_pair @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).

thf(46,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(49,plain,
    $false,
    inference(cvc4,[status(thm)],[17,7,15,20,46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU151+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n014.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 10:26:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.17/0.98  % [INFO] 	 Parsing done (115ms). 
% 1.34/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.68/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.68/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.27  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.95/1.29  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.95/1.30  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.95/1.30  % [INFO] 	 Type checking passed. 
% 1.95/1.30  % [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 ... 
% 3.34/1.76  % External prover 'cvc4' found a proof!
% 3.34/1.76  % [INFO] 	 Killing All external provers ... 
% 3.34/1.76  % Time passed: 1221ms (effective reasoning time: 762ms)
% 3.34/1.76  % 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)>
% 3.34/1.76  % Axioms used in derivation (4): commutativity_k2_tarski, antisymmetry_r2_hidden, d2_tarski, dt_k2_tarski
% 3.34/1.76  % No. of inferences in proof: 12
% 3.34/1.76  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1221 ms resp. 762 ms w/o parsing
% 3.39/1.79  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.79  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------