TSTP Solution File: SYN066+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN066+1 : TPTP v8.1.0. Bugfixed v3.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n021.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 08:23:14 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   56 (  35 unt;   8 typ;   0 def)
%            Number of atoms       :  216 (  53 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  476 (  67   ~;  46   |;   8   &; 347   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :  103 (   0   ^  86   !;  17   ?; 103   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_big_p,type,
    big_p: $i > $i > $o ).

thf(tp_big_q,type,
    big_q: $i > $i > $o ).

thf(tp_big_r,type,
    big_r: $i > $i > $o ).

thf(tp_sK1_X,type,
    sK1_X: $i ).

thf(tp_sK2_Y,type,
    sK2_Y: $i > $i > $i ).

thf(tp_sK3_W,type,
    sK3_W: $i > $i ).

thf(tp_sK4_SY15,type,
    sK4_SY15: $i > $i > $i ).

thf(tp_sK5_SY16,type,
    sK5_SY16: $i > $i > $i ).

thf(1,axiom,
    ( ? [X: $i,Y: $i] : ( big_q @ X @ Y )
   => ! [Z: $i] : ( big_r @ Z @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_3) ).

thf(2,axiom,
    ! [X: $i,Z: $i] :
      ( ~ ( big_p @ X @ Z )
     => ? [Y: $i] : ( big_q @ Y @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_2) ).

thf(3,axiom,
    ! [Z: $i] :
    ? [W: $i] :
    ! [X: $i] :
    ? [Y: $i] :
      ( ( ( big_p @ X @ Z )
       => ( big_p @ Y @ W ) )
      & ( big_p @ Y @ Z )
      & ( ( big_p @ Y @ W )
       => ? [U: $i] : ( big_q @ U @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37_1) ).

thf(4,conjecture,
    ! [X: $i] :
    ? [Y: $i] : ( big_r @ X @ Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel37) ).

thf(5,negated_conjecture,
    ( ( ! [X: $i] :
        ? [Y: $i] : ( big_r @ X @ Y ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[4]) ).

thf(6,plain,
    ( ( ! [X: $i] :
        ? [Y: $i] : ( big_r @ X @ Y ) )
    = $false ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ? [X: $i,Y: $i] : ( big_q @ X @ Y )
     => ! [Z: $i] : ( big_r @ Z @ Z ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(8,plain,
    ( ( ! [X: $i,Z: $i] :
          ( ~ ( big_p @ X @ Z )
         => ? [Y: $i] : ( big_q @ Y @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(9,plain,
    ( ( ! [Z: $i] :
        ? [W: $i] :
        ! [X: $i] :
        ? [Y: $i] :
          ( ( ( big_p @ X @ Z )
           => ( big_p @ Y @ W ) )
          & ( big_p @ Y @ Z )
          & ( ( big_p @ Y @ W )
           => ? [U: $i] : ( big_q @ U @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(10,plain,
    ( ( ? [SY13: $i] : ( big_r @ sK1_X @ SY13 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ~ ? [SY13: $i] : ( big_r @ sK1_X @ SY13 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ! [SY13: $i] :
          ~ ( big_r @ sK1_X @ SY13 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(13,plain,
    ( ( ! [X: $i,Y: $i] :
          ~ ( big_q @ X @ Y )
      | ! [Z: $i] : ( big_r @ Z @ Z ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(14,plain,
    ( ( ! [X: $i,Z: $i] :
          ( ( big_p @ X @ Z )
          | ( big_q @ ( sK2_Y @ Z @ X ) @ Z ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(15,plain,
    ( ( ! [Z: $i,SY14: $i] :
          ( ( ~ ( big_p @ SY14 @ Z )
            | ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ ( sK3_W @ Z ) ) )
          & ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ Z )
          & ( ~ ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ ( sK3_W @ Z ) )
            | ( big_q @ ( sK5_SY16 @ SY14 @ Z ) @ ( sK3_W @ Z ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(16,plain,
    ( ( ! [Z: $i,SY14: $i] :
          ( ( ~ ( big_p @ SY14 @ Z )
            | ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ ( sK3_W @ Z ) ) )
          & ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ Z )
          & ( ~ ( big_p @ ( sK4_SY15 @ SY14 @ Z ) @ ( sK3_W @ Z ) )
            | ( big_q @ ( sK5_SY16 @ SY14 @ Z ) @ ( sK3_W @ Z ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(17,plain,
    ( ( ! [X: $i,Z: $i] :
          ( ( big_p @ X @ Z )
          | ( big_q @ ( sK2_Y @ Z @ X ) @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i] :
          ~ ( big_q @ X @ Y )
      | ! [Z: $i] : ( big_r @ Z @ Z ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(19,plain,
    ( ( ! [SY13: $i] :
          ~ ( big_r @ sK1_X @ SY13 ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(20,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ~ ( ~ ( ~ ( big_p @ SX1 @ SX0 )
                      | ( big_p @ ( sK4_SY15 @ SX1 @ SX0 ) @ ( sK3_W @ SX0 ) ) )
                  | ~ ( big_p @ ( sK4_SY15 @ SX1 @ SX0 ) @ SX0 ) )
            | ~ ( ~ ( big_p @ ( sK4_SY15 @ SX1 @ SX0 ) @ ( sK3_W @ SX0 ) )
                | ( big_q @ ( sK5_SY16 @ SX1 @ SX0 ) @ ( sK3_W @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(21,plain,
    ! [SV1: $i] :
      ( ( ! [SY18: $i] :
            ( ( big_p @ SV1 @ SY18 )
            | ( big_q @ ( sK2_Y @ SY18 @ SV1 ) @ SY18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(22,plain,
    ( ( ( ! [X: $i,Y: $i] :
            ~ ( big_q @ X @ Y ) )
      = $true )
    | ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV2: $i] :
      ( ( ~ ( big_r @ sK1_X @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(24,plain,
    ! [SV3: $i] :
      ( ( ! [SY19: $i] :
            ~ ( ~ ~ ( ~ ( ~ ( big_p @ SY19 @ SV3 )
                        | ( big_p @ ( sK4_SY15 @ SY19 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
                    | ~ ( big_p @ ( sK4_SY15 @ SY19 @ SV3 ) @ SV3 ) )
              | ~ ( ~ ( big_p @ ( sK4_SY15 @ SY19 @ SV3 ) @ ( sK3_W @ SV3 ) )
                  | ( big_q @ ( sK5_SY16 @ SY19 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( big_p @ SV1 @ SV4 )
        | ( big_q @ ( sK2_Y @ SV4 @ SV1 ) @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV5: $i] :
      ( ( ( ! [SY20: $i] :
              ~ ( big_q @ SV5 @ SY20 ) )
        = $true )
      | ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV2: $i] :
      ( ( big_r @ sK1_X @ SV2 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( ~ ~ ( ~ ( ~ ( big_p @ SV6 @ SV3 )
                      | ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
                  | ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) )
            | ~ ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
                | ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( big_p @ SV1 @ SV4 )
        = $true )
      | ( ( big_q @ ( sK2_Y @ SV4 @ SV1 ) @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV7: $i,SV5: $i] :
      ( ( ( ~ ( big_q @ SV5 @ SV7 ) )
        = $true )
      | ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ~ ( ~ ( ~ ( big_p @ SV6 @ SV3 )
                  | ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
              | ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) )
        | ~ ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
            | ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV7: $i,SV5: $i] :
      ( ( ( big_q @ SV5 @ SV7 )
        = $false )
      | ( ( ! [Z: $i] : ( big_r @ Z @ Z ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(33,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ~ ( ~ ( ~ ( big_p @ SV6 @ SV3 )
                  | ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
              | ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
            | ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(35,plain,
    ! [SV7: $i,SV5: $i,SV8: $i] :
      ( ( ( big_r @ SV8 @ SV8 )
        = $true )
      | ( ( big_q @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( ~ ( ~ ( big_p @ SV6 @ SV3 )
                | ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
            | ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(37,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
        | ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(38,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( ~ ( big_p @ SV6 @ SV3 )
            | ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
        | ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
        = $true )
      | ( ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(40,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( ~ ( big_p @ SV6 @ SV3 )
            | ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(41,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(42,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
        = $false )
      | ( ( big_q @ ( sK5_SY16 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(43,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( big_p @ SV6 @ SV3 )
        | ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(44,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ SV3 )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(45,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( ~ ( big_p @ SV6 @ SV3 ) )
        = $true )
      | ( ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(46,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( big_p @ SV6 @ SV3 )
        = $false )
      | ( ( big_p @ ( sK4_SY15 @ SV6 @ SV3 ) @ ( sK3_W @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(47,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[27,46,44,42,35,29]) ).

thf(48,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN066+1 : TPTP v8.1.0. Bugfixed v3.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % 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 : Tue Jul 12 09:04:09 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 3
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.20/0.39  
% 0.20/0.39  ********************************
% 0.20/0.39  *   All subproblems solved!    *
% 0.20/0.39  ********************************
% 0.20/0.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.39  
% 0.20/0.39  %**** Beginning of derivation protocol ****
% 0.20/0.39  % SZS output start CNFRefutation
% See solution above
% 0.20/0.39  
% 0.20/0.39  %**** End of derivation protocol ****
% 0.20/0.39  %**** no. of clauses in derivation: 48 ****
% 0.20/0.39  %**** clause counter: 47 ****
% 0.20/0.39  
% 0.20/0.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:47,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------