TSTP Solution File: SYO234^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO234^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n020.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 : Thu Jul 21 17:32:53 EDT 2022

% Result   : Theorem 0.19s 0.37s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   35 (  22 unt;   6 typ;   0 def)
%            Number of atoms       :  141 (  50 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  295 (  17   ~;  40   |;   0   &; 238   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   64 (  64   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   50 (  21   ^  25   !;   4   ?;  50   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c,type,
    c: $tType ).

thf(tp_d,type,
    d: $tType ).

thf(tp_cA,type,
    cA: c > d > $o ).

thf(tp_cB,type,
    cB: d > c > $o ).

thf(tp_sK1_SV2,type,
    sK1_SV2: ( c > d > $o ) > c ).

thf(tp_sK2_SV3,type,
    sK2_SV3: ( c > d > $o ) > d ).

thf(1,conjecture,
    ? [Xu: c > d > $o] :
      ( Xu
      = ( ^ [Xx: c,Xy: d] :
            ( ( cA @ Xx @ Xy )
            | ( cB @ Xy @ Xx ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSV4) ).

thf(2,negated_conjecture,
    ( ( ? [Xu: c > d > $o] :
          ( Xu
          = ( ^ [Xx: c,Xy: d] :
                ( ( cA @ Xx @ Xy )
                | ( cB @ Xy @ Xx ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ? [Xu: c > d > $o] :
          ( Xu
          = ( ^ [Xx: c,Xy: d] :
                ( ( cA @ Xx @ Xy )
                | ( cB @ Xy @ Xx ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ~ ? [Xu: c > d > $o] :
            ( Xu
            = ( ^ [Xx: c,Xy: d] :
                  ( ( cA @ Xx @ Xy )
                  | ( cB @ Xy @ Xx ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xu: c > d > $o] :
          ( Xu
         != ( ^ [Xx: c,Xy: d] :
                ( ( cA @ Xx @ Xy )
                | ( cB @ Xy @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [Xu: c > d > $o] :
          ( Xu
         != ( ^ [Xx: c,Xy: d] :
                ( ( cA @ Xx @ Xy )
                | ( cB @ Xy @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(7,plain,
    ! [SV1: c > d > $o] :
      ( ( ( SV1
         != ( ^ [Xx: c,Xy: d] :
                ( ( cA @ Xx @ Xy )
                | ( cB @ Xy @ Xx ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6]) ).

thf(8,plain,
    ! [SV1: c > d > $o] :
      ( ( SV1
        = ( ^ [Xx: c,Xy: d] :
              ( ( cA @ Xx @ Xy )
              | ( cB @ Xy @ Xx ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7]) ).

thf(9,plain,
    ! [SV1: c > d > $o] :
      ( ( ! [SV2: c] :
            ( ( SV1 @ SV2 )
            = ( ^ [SY5: d] :
                  ( ( cA @ SV2 @ SY5 )
                  | ( cB @ SY5 @ SV2 ) ) ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[8]) ).

thf(10,plain,
    ! [SV1: c > d > $o] :
      ( ( SV1
        = ( ^ [Xx: c,Xy: d] :
              ( ( cA @ Xx @ Xy )
              | ( cB @ Xy @ Xx ) ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[8]) ).

thf(11,plain,
    ! [SV1: c > d > $o] :
      ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
        = ( ^ [SY6: d] :
              ( ( cA @ ( sK1_SV2 @ SV1 ) @ SY6 )
              | ( cB @ SY6 @ ( sK1_SV2 @ SV1 ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[9]) ).

thf(12,plain,
    ! [SV1: c > d > $o] :
      ( ( ! [SV3: d] :
            ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ SV3 )
            = ( ( cA @ ( sK1_SV2 @ SV1 ) @ SV3 )
              | ( cB @ SV3 @ ( sK1_SV2 @ SV1 ) ) ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[11]) ).

thf(13,plain,
    ! [SV1: c > d > $o] :
      ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
        = ( ^ [SY6: d] :
              ( ( cA @ ( sK1_SV2 @ SV1 ) @ SY6 )
              | ( cB @ SY6 @ ( sK1_SV2 @ SV1 ) ) ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[11]) ).

thf(14,plain,
    ! [SV1: c > d > $o] :
      ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
          | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[12]) ).

thf(15,plain,
    ! [SV1: c > d > $o] :
      ( ( ~ ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
            | ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
            | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) )
        | ~ ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
            | ~ ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
                | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[14]) ).

thf(16,plain,
    ! [SV1: c > d > $o] :
      ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
          | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[14]) ).

thf(17,plain,
    ! [SV1: c > d > $o] :
      ( ( ~ ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
            | ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
            | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV1: c > d > $o] :
      ( ( ~ ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
            | ~ ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
                | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV1: c > d > $o] :
      ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        | ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV1: c > d > $o] :
      ( ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        | ~ ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
            | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV1: c > d > $o] :
      ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = $true )
      | ( ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
          | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[19]) ).

thf(22,plain,
    ! [SV1: c > d > $o] :
      ( ( ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
              | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV1: c > d > $o] :
      ( ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = $true )
      | ( ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) )
        = $true )
      | ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[21]) ).

thf(24,plain,
    ! [SV1: c > d > $o] :
      ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = $false )
      | ( ( ~ ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
              | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV1: c > d > $o] :
      ( ( ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
          | ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) ) )
        = $false )
      | ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(26,plain,
    ! [SV1: c > d > $o] :
      ( ( ( cA @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = $false )
      | ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(27,plain,
    ! [SV1: c > d > $o] :
      ( ( ( cB @ ( sK2_SV3 @ SV1 ) @ ( sK1_SV2 @ SV1 ) )
        = $false )
      | ( ( SV1 @ ( sK1_SV2 @ SV1 ) @ ( sK2_SV3 @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(28,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[10,27,26,23,16,13]) ).

thf(29,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYO234^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jul  9 12:31:28 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)
% 0.19/0.37  ********************************
% 0.19/0.37  *   All subproblems solved!    *
% 0.19/0.37  ********************************
% 0.19/0.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.38  
% 0.19/0.38  %**** Beginning of derivation protocol ****
% 0.19/0.38  % SZS output start CNFRefutation
% See solution above
% 0.19/0.38  
% 0.19/0.38  %**** End of derivation protocol ****
% 0.19/0.38  %**** no. of clauses in derivation: 29 ****
% 0.19/0.38  %**** clause counter: 28 ****
% 0.19/0.38  
% 0.19/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:28,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------