TSTP Solution File: SYN346+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN346+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n008.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 08:25:25 EDT 2022

% Result   : Theorem 0.23s 0.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   39 (  27 unt;   5 typ;   0 def)
%            Number of atoms       :  201 (  38 equ;   0 cnn)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives :  640 ( 129   ~;  61   |;  18   &; 420   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   83 (   0   ^  71   !;  12   ?;  83   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_big_f,type,
    big_f: $i > $i > $o ).

thf(tp_sK1_X1,type,
    sK1_X1: $i ).

thf(tp_sK2_X2,type,
    sK2_X2: $i ).

thf(tp_sK3_SY13,type,
    sK3_SY13: $i > $i > $i ).

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

thf(1,conjecture,
    ! [X1: $i,X2: $i] :
    ? [Y1: $i,Y2: $i] :
    ! [Z1: $i,Z2: $i] :
      ( ( big_f @ X2 @ Z1 )
     => ( ( big_f @ Y1 @ Z2 )
       => ( ( ( big_f @ Y1 @ Z1 )
            & ( big_f @ Y2 @ Z1 ) )
          | ( ( big_f @ X2 @ Z2 )
            & ( big_f @ Y2 @ Z2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_17_2) ).

thf(2,negated_conjecture,
    ( ( ! [X1: $i,X2: $i] :
        ? [Y1: $i,Y2: $i] :
        ! [Z1: $i,Z2: $i] :
          ( ( big_f @ X2 @ Z1 )
         => ( ( big_f @ Y1 @ Z2 )
           => ( ( ( big_f @ Y1 @ Z1 )
                & ( big_f @ Y2 @ Z1 ) )
              | ( ( big_f @ X2 @ Z2 )
                & ( big_f @ Y2 @ Z2 ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [X1: $i,X2: $i] :
        ? [Y1: $i,Y2: $i] :
        ! [Z1: $i,Z2: $i] :
          ( ( big_f @ X2 @ Z1 )
         => ( ( big_f @ Y1 @ Z2 )
           => ( ( ( big_f @ Y1 @ Z1 )
                & ( big_f @ Y2 @ Z1 ) )
              | ( ( big_f @ X2 @ Z2 )
                & ( big_f @ Y2 @ Z2 ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [X2: $i] :
        ? [Y1: $i,Y2: $i] :
        ! [Z1: $i,Z2: $i] :
          ( ( big_f @ X2 @ Z1 )
         => ( ( big_f @ Y1 @ Z2 )
           => ( ( ( big_f @ Y1 @ Z1 )
                & ( big_f @ Y2 @ Z1 ) )
              | ( ( big_f @ X2 @ Z2 )
                & ( big_f @ Y2 @ Z2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ? [SY11: $i,SY12: $i] :
        ! [SY13: $i,SY14: $i] :
          ( ( big_f @ sK2_X2 @ SY13 )
         => ( ( big_f @ SY11 @ SY14 )
           => ( ( ( big_f @ SY11 @ SY13 )
                & ( big_f @ SY12 @ SY13 ) )
              | ( ( big_f @ sK2_X2 @ SY14 )
                & ( big_f @ SY12 @ SY14 ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ~ ? [SY11: $i,SY12: $i] :
          ! [SY13: $i,SY14: $i] :
            ( ( big_f @ sK2_X2 @ SY13 )
           => ( ( big_f @ SY11 @ SY14 )
             => ( ( ( big_f @ SY11 @ SY13 )
                  & ( big_f @ SY12 @ SY13 ) )
                | ( ( big_f @ sK2_X2 @ SY14 )
                  & ( big_f @ SY12 @ SY14 ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY11: $i,SY12: $i] :
          ( ( big_f @ sK2_X2 @ ( sK3_SY13 @ SY12 @ SY11 ) )
          & ( big_f @ SY11 @ ( sK4_SY15 @ SY12 @ SY11 ) )
          & ( ~ ( big_f @ SY11 @ ( sK3_SY13 @ SY12 @ SY11 ) )
            | ~ ( big_f @ SY12 @ ( sK3_SY13 @ SY12 @ SY11 ) ) )
          & ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SY12 @ SY11 ) )
            | ~ ( big_f @ SY12 @ ( sK4_SY15 @ SY12 @ SY11 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [SY11: $i,SY12: $i] :
          ( ( big_f @ sK2_X2 @ ( sK3_SY13 @ SY12 @ SY11 ) )
          & ( big_f @ SY11 @ ( sK4_SY15 @ SY12 @ SY11 ) )
          & ( ~ ( big_f @ SY11 @ ( sK3_SY13 @ SY12 @ SY11 ) )
            | ~ ( big_f @ SY12 @ ( sK3_SY13 @ SY12 @ SY11 ) ) )
          & ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SY12 @ SY11 ) )
            | ~ ( big_f @ SY12 @ ( sK4_SY15 @ SY12 @ SY11 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( big_f @ sK2_X2 @ ( sK3_SY13 @ SX1 @ SX0 ) )
            | ~ ~ ( ~ ( big_f @ SX0 @ ( sK4_SY15 @ SX1 @ SX0 ) )
                  | ~ ~ ( ~ ( ~ ( big_f @ SX0 @ ( sK3_SY13 @ SX1 @ SX0 ) )
                            | ~ ( big_f @ SX1 @ ( sK3_SY13 @ SX1 @ SX0 ) ) )
                        | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SX1 @ SX0 ) )
                            | ~ ( big_f @ SX1 @ ( sK4_SY15 @ SX1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(10,plain,
    ! [SV1: $i] :
      ( ( ! [SY16: $i] :
            ~ ( ~ ( big_f @ sK2_X2 @ ( sK3_SY13 @ SY16 @ SV1 ) )
              | ~ ~ ( ~ ( big_f @ SV1 @ ( sK4_SY15 @ SY16 @ SV1 ) )
                    | ~ ~ ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SY16 @ SV1 ) )
                              | ~ ( big_f @ SY16 @ ( sK3_SY13 @ SY16 @ SV1 ) ) )
                          | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SY16 @ SV1 ) )
                              | ~ ( big_f @ SY16 @ ( sK4_SY15 @ SY16 @ SV1 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[9]) ).

thf(11,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( big_f @ sK2_X2 @ ( sK3_SY13 @ SV2 @ SV1 ) )
            | ~ ~ ( ~ ( big_f @ SV1 @ ( sK4_SY15 @ SV2 @ SV1 ) )
                  | ~ ~ ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
                            | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
                        | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
                            | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(12,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( big_f @ sK2_X2 @ ( sK3_SY13 @ SV2 @ SV1 ) )
        | ~ ~ ( ~ ( big_f @ SV1 @ ( sK4_SY15 @ SV2 @ SV1 ) )
              | ~ ~ ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
                        | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
                    | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
                        | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11]) ).

thf(13,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( big_f @ sK2_X2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(14,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ~ ( ~ ( big_f @ SV1 @ ( sK4_SY15 @ SV2 @ SV1 ) )
              | ~ ~ ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
                        | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
                    | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
                        | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( big_f @ sK2_X2 @ ( sK3_SY13 @ SV2 @ SV1 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ( big_f @ SV1 @ ( sK4_SY15 @ SV2 @ SV1 ) )
            | ~ ~ ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
                      | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
                  | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
                      | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(17,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( big_f @ SV1 @ ( sK4_SY15 @ SV2 @ SV1 ) )
        | ~ ~ ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
                  | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
              | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
                  | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(18,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( big_f @ SV1 @ ( sK4_SY15 @ SV2 @ SV1 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(19,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ~ ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
                  | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
              | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
                  | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( big_f @ SV1 @ ( sK4_SY15 @ SV2 @ SV1 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
                | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
            | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
                | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(22,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
            | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
        | ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
            | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(23,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
            | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(24,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
            | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
        | ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(26,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
        | ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(27,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ~ ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
        = $false )
      | ( ( ~ ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
        = $false )
      | ( ( ~ ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(31,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_f @ SV2 @ ( sK3_SY13 @ SV2 @ SV1 ) )
        = $false )
      | ( ( big_f @ SV1 @ ( sK3_SY13 @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(32,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( big_f @ SV2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
        = $false )
      | ( ( big_f @ sK2_X2 @ ( sK4_SY15 @ SV2 @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(33,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[15,32,31,20]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SYN346+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.15  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36  % Computer : n008.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Tue Jul 12 01:27:23 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.37  
% 0.15/0.37   No.of.Axioms: 0
% 0.15/0.37  
% 0.15/0.37   Length.of.Defs: 0
% 0.15/0.37  
% 0.15/0.37   Contains.Choice.Funs: false
% 0.15/0.37  (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.23/0.41  
% 0.23/0.41  ********************************
% 0.23/0.41  *   All subproblems solved!    *
% 0.23/0.41  ********************************
% 0.23/0.41  % SZS status Theorem for /export/starexec/sandbox2/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: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)
% 0.23/0.41  
% 0.23/0.41  %**** Beginning of derivation protocol ****
% 0.23/0.41  % SZS output start CNFRefutation
% See solution above
% 0.23/0.41  
% 0.23/0.41  %**** End of derivation protocol ****
% 0.23/0.41  %**** no. of clauses in derivation: 34 ****
% 0.23/0.41  %**** clause counter: 33 ****
% 0.23/0.41  
% 0.23/0.41  % SZS status Theorem for /export/starexec/sandbox2/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: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)
%------------------------------------------------------------------------------