TSTP Solution File: SEU150+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n028.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  : 600s
% DateTime : Tue Jul 19 12:07:10 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   39 (  29 unt;   5 typ;   0 def)
%            Number of atoms       :  111 (  72 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   94 (   8   ~;   7   |;   0   &;  71   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   49 (   0   ^  49   !;   0   ?;  49   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK2_SY8,type,
    sK2_SY8: $i ).

thf(tp_sK3_SY10,type,
    sK3_SY10: $i ).

thf(tp_singleton,type,
    singleton: $i > $i ).

thf(tp_unordered_pair,type,
    unordered_pair: $i > $i > $i ).

thf(1,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( singleton @ A )
        = ( unordered_pair @ B @ C ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).

thf(2,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).

thf(3,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).

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(5,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( singleton @ A )
        = ( unordered_pair @ B @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).

thf(6,negated_conjecture,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( singleton @ A )
            = ( unordered_pair @ B @ C ) )
         => ( B = C ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[5]) ).

thf(7,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( singleton @ A )
            = ( unordered_pair @ B @ C ) )
         => ( B = C ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( singleton @ A )
            = ( unordered_pair @ B @ C ) )
         => ( A = B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(9,plain,
    $true = $true,
    inference(unfold_def,[status(thm)],[2]) ).

thf(10,plain,
    $true = $true,
    inference(unfold_def,[status(thm)],[3]) ).

thf(11,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( unordered_pair @ A @ B )
          = ( unordered_pair @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(12,plain,
    ( ( ! [SY8: $i,SY9: $i] :
          ( ( ( singleton @ sK1_A )
            = ( unordered_pair @ SY8 @ SY9 ) )
         => ( SY8 = SY9 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[7]) ).

thf(13,plain,
    ( ( ! [SY10: $i] :
          ( ( ( singleton @ sK1_A )
            = ( unordered_pair @ sK2_SY8 @ SY10 ) )
         => ( sK2_SY8 = SY10 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[12]) ).

thf(14,plain,
    ( ( ( ( singleton @ sK1_A )
        = ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
     => ( sK2_SY8 = sK3_SY10 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[13]) ).

thf(15,plain,
    ( ( ( singleton @ sK1_A )
      = ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[14]) ).

thf(16,plain,
    ( ( sK2_SY8 = sK3_SY10 )
    = $false ),
    inference(standard_cnf,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ( sK2_SY8 != sK3_SY10 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[16]) ).

thf(18,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( singleton @ A )
             != ( unordered_pair @ B @ C ) )
          | ( A = B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(19,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( unordered_pair @ A @ B )
          = ( unordered_pair @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(20,plain,
    $true = $true,
    inference(copy,[status(thm)],[10]) ).

thf(21,plain,
    $true = $true,
    inference(copy,[status(thm)],[9]) ).

thf(22,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( singleton @ A )
             != ( unordered_pair @ B @ C ) )
          | ( A = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ( singleton @ sK1_A )
      = ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(24,plain,
    ( ( ( sK2_SY8 != sK3_SY10 ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(25,plain,
    ! [SV1: $i] :
      ( ( ! [SY11: $i] :
            ( ( unordered_pair @ SV1 @ SY11 )
            = ( unordered_pair @ SY11 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(26,plain,
    ! [SV2: $i] :
      ( ( ! [SY12: $i] :
            ( ! [SY13: $i] :
                ( ( singleton @ SV2 )
               != ( unordered_pair @ SY12 @ SY13 ) )
            | ( SV2 = SY12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( sK2_SY8 = sK3_SY10 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( unordered_pair @ SV1 @ SV3 )
        = ( unordered_pair @ SV3 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ! [SY14: $i] :
            ( ( singleton @ SV2 )
           != ( unordered_pair @ SV4 @ SY14 ) )
        | ( SV2 = SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ! [SY14: $i] :
              ( ( singleton @ SV2 )
             != ( unordered_pair @ SV4 @ SY14 ) ) )
        = $true )
      | ( ( SV2 = SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(31,plain,
    ! [SV5: $i,SV4: $i,SV2: $i] :
      ( ( ( ( ( singleton @ SV2 )
           != ( unordered_pair @ SV4 @ SV5 ) ) )
        = $true )
      | ( ( SV2 = SV4 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(32,plain,
    ! [SV5: $i,SV4: $i,SV2: $i] :
      ( ( ( ( singleton @ SV2 )
          = ( unordered_pair @ SV4 @ SV5 ) )
        = $false )
      | ( ( SV2 = SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(33,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[20,32,28,27,23,21]) ).

thf(34,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun 19 11:53:15 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 4
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.37  
% 0.13/0.37  ********************************
% 0.13/0.37  *   All subproblems solved!    *
% 0.13/0.37  ********************************
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.37  
% 0.13/0.37  %**** Beginning of derivation protocol ****
% 0.13/0.37  % SZS output start CNFRefutation
% See solution above
% 0.13/0.37  
% 0.13/0.37  %**** End of derivation protocol ****
% 0.13/0.37  %**** no. of clauses in derivation: 34 ****
% 0.13/0.37  %**** clause counter: 33 ****
% 0.13/0.37  
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------