TSTP Solution File: SYO227^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO227^5 : 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 : 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 : Thu Jul 21 17:32:51 EDT 2022

% Result   : Theorem 0.21s 0.44s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   56 (  20 unt;   4 typ;   0 def)
%            Number of atoms       :  289 ( 153 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  267 (  54   ~;  65   |;  13   &; 125   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   5 con; 0-2 aty)
%            Number of variables   :   54 (   0   ^  49   !;   5   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $i ).

thf(tp_b,type,
    b: $i ).

thf(tp_c,type,
    c: $i ).

thf(tp_c_less_,type,
    c_less_: $i > $i > $o ).

thf(1,conjecture,
    ( ! [Xx: $i,Xy: $i] :
        ( ( c_less_ @ Xx @ Xy )
       => ( Xx != Xy ) )
   => ( ( ( c_less_ @ a @ b )
        & ( c_less_ @ b @ c ) )
     => ? [A: $i > $o] :
          ( ~ ( A @ a )
          & ( A @ b )
          & ~ ( A @ c ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE4_W_AX) ).

thf(2,negated_conjecture,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( c_less_ @ Xx @ Xy )
         => ( Xx != Xy ) )
     => ( ( ( c_less_ @ a @ b )
          & ( c_less_ @ b @ c ) )
       => ? [A: $i > $o] :
            ( ~ ( A @ a )
            & ( A @ b )
            & ~ ( A @ c ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( c_less_ @ Xx @ Xy )
         => ( Xx != Xy ) )
     => ( ( ( c_less_ @ a @ b )
          & ( c_less_ @ b @ c ) )
       => ? [A: $i > $o] :
            ( ~ ( A @ a )
            & ( A @ b )
            & ~ ( A @ c ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( c_less_ @ Xx @ Xy )
         => ( Xx != Xy ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( c_less_ @ a @ b )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( c_less_ @ b @ c )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ? [A: $i > $o] :
          ( ~ ( A @ a )
          & ( A @ b )
          & ~ ( A @ c ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ~ ? [A: $i > $o] :
            ( ~ ( A @ a )
            & ( A @ b )
            & ~ ( A @ c ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [A: $i > $o] :
          ( ( A @ a )
          | ~ ( A @ b )
          | ( A @ c ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ~ ( c_less_ @ Xx @ Xy )
          | ( Xx != Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(11,plain,
    ( ( c_less_ @ b @ c )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(12,plain,
    ( ( c_less_ @ a @ b )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(13,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ~ ( c_less_ @ Xx @ Xy )
          | ( Xx != Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ! [A: $i > $o] :
          ( ( A @ a )
          | ~ ( A @ b )
          | ( A @ c ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(15,plain,
    ! [SV1: $i] :
      ( ( ! [SY3: $i] :
            ( ~ ( c_less_ @ SV1 @ SY3 )
            | ( SV1 != SY3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ a )
        | ~ ( SV2 @ b )
        | ( SV2 @ c ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(17,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ~ ( c_less_ @ SV1 @ SV3 )
        | ( SV1 != SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV2: $i > $o] :
      ( ( ( ( SV2 @ a )
          | ~ ( SV2 @ b ) )
        = $true )
      | ( ( SV2 @ c )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[16]) ).

thf(19,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( c_less_ @ SV1 @ SV3 ) )
        = $true )
      | ( ( ( SV1 != SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ a )
        = $true )
      | ( ( ~ ( SV2 @ b ) )
        = $true )
      | ( ( SV2 @ c )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( c_less_ @ SV1 @ SV3 )
        = $false )
      | ( ( ( SV1 != SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(22,plain,
    ! [SV2: $i > $o] :
      ( ( ( SV2 @ b )
        = $false )
      | ( ( SV2 @ a )
        = $true )
      | ( ( SV2 @ c )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( SV1 = SV3 )
        = $false )
      | ( ( c_less_ @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(24,plain,
    ( ( ( b = b )
      = $false )
    | ( ( a = b )
      = $true )
    | ( ( c = b )
      = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[22:[bind(SV2,$thf( ^ [SV4: $i] : ( SV4 = b ) ))]]) ).

thf(25,plain,
    ( ( ( a = b )
      = $true )
    | ( ( c = b )
      = $true ) ),
    inference(sim,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV6: $i > $o] :
      ( ( ( ~ ( SV6 @ b ) )
        = $false )
      | ( ( ~ ( SV6 @ a ) )
        = $true )
      | ( ( ~ ( SV6 @ c ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[22:[bind(SV2,$thf( ^ [SV5: $i] : ~ ( SV6 @ SV5 ) ))]]) ).

thf(30,plain,
    ( ( ( b = b )
      = $false )
    | ( ( a = b )
      = $true )
    | ( ( c = b )
      = $true ) ),
    inference(prim_subst,[status(thm)],[22:[bind(SV2,$thf( ^ [SV10: $i] : ( SV10 = b ) ))]]) ).

thf(32,plain,
    ( ( ( c = b )
      = $true )
    | ( ( ( a = b )
        = ( c = b ) )
      = $false ) ),
    inference(fac_restr,[status(thm)],[25]) ).

thf(33,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( c_less_ @ SV1 @ SV3 )
        = $false )
      | ( ( ( SV1 = SV3 )
          = ( c_less_ @ SV1 @ SV3 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[23]) ).

thf(34,plain,
    ( ( ( ~ ( ( a = b )
            | ( c = b ) )
        | ~ ( ( a != b )
            | ( c != b ) ) )
      = $false )
    | ( ( c = b )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[32]) ).

thf(35,plain,
    ( ( ( ( a = b )
        = ( c = b ) )
      = $false )
    | ( ( c = b )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( ( SV1 = SV3 )
              | ( c_less_ @ SV1 @ SV3 ) )
          | ~ ( ( SV1 != SV3 )
              | ~ ( c_less_ @ SV1 @ SV3 ) ) )
        = $false )
      | ( ( c_less_ @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[33]) ).

thf(38,plain,
    ( ( ( ~ ( ( a = b )
            | ( c = b ) ) )
      = $false )
    | ( ( c = b )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( ( SV1 != SV3 )
              | ~ ( c_less_ @ SV1 @ SV3 ) ) )
        = $false )
      | ( ( c_less_ @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(42,plain,
    ( ( ( ( a = b )
        | ( c = b ) )
      = $true )
    | ( ( c = b )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ( SV1 != SV3 )
          | ~ ( c_less_ @ SV1 @ SV3 ) )
        = $true )
      | ( ( c_less_ @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(46,plain,
    ( ( ( a = b )
      = $true )
    | ( ( c = b )
      = $true )
    | ( ( c = b )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(49,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ( SV1 != SV3 ) )
        = $true )
      | ( ( ~ ( c_less_ @ SV1 @ SV3 ) )
        = $true )
      | ( ( c_less_ @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( SV1 = SV3 )
        = $false )
      | ( ( ~ ( c_less_ @ SV1 @ SV3 ) )
        = $true )
      | ( ( c_less_ @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( c_less_ @ SV1 @ SV3 )
        = $false )
      | ( ( SV1 = SV3 )
        = $false )
      | ( ( c_less_ @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(54,plain,
    ( ( ( c = b )
      = $true )
    | ( ( a = b )
      = $false )
    | ( ( b = c )
      = $false ) ),
    inference(extuni,[status(esa)],[35]) ).

thf(55,plain,
    ( ( ( c = b )
      = $true )
    | ( ( a = c )
      = $false ) ),
    inference(extuni,[status(esa)],[35]) ).

thf(56,plain,
    ! [SV3: $i] :
      ( ( ( c_less_ @ SV3 @ SV3 )
        = $false )
      | ( ( c_less_ @ SV3 @ SV3 )
        = $false ) ),
    inference(extuni,[status(esa)],[53:[bind(SV1,$thf( SV3 ))]]) ).

thf(57,plain,
    ! [SV3: $i] :
      ( ( c_less_ @ SV3 @ SV3 )
      = $false ),
    inference(extuni,[status(esa)],[23:[bind(SV1,$thf( SV3 ))]]) ).

thf(58,plain,
    ! [SV6: $i > $o] :
      ( ( ( SV6 @ b )
        = $true )
      | ( ( ~ ( SV6 @ a ) )
        = $true )
      | ( ( ~ ( SV6 @ c ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(59,plain,
    ! [SV6: $i > $o] :
      ( ( ( SV6 @ a )
        = $false )
      | ( ( SV6 @ b )
        = $true )
      | ( ( ~ ( SV6 @ c ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(60,plain,
    ! [SV6: $i > $o] :
      ( ( ( SV6 @ c )
        = $false )
      | ( ( SV6 @ b )
        = $true )
      | ( ( SV6 @ a )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(61,plain,
    ( ( ( c = b )
      = $true )
    | ( ( a = b )
      = $true ) ),
    inference(extuni,[status(esa)],[30]) ).

thf(62,plain,
    ( ( ( a = b )
      = $true )
    | ( ( c = b )
      = $true ) ),
    inference(sim,[status(thm)],[46]) ).

thf(63,plain,
    ! [SV3: $i] :
      ( ( c_less_ @ SV3 @ SV3 )
      = $false ),
    inference(sim,[status(thm)],[56]) ).

thf(64,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[11,63,62,61,60,57,55,54,25,23,22,12]) ).

thf(65,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYO227^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36  % Computer : n028.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Fri Jul  8 18:28:10 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  
% 0.14/0.36   No.of.Axioms: 0
% 0.14/0.36  
% 0.14/0.36   Length.of.Defs: 0
% 0.14/0.36  
% 0.14/0.36   Contains.Choice.Funs: false
% 0.14/0.37  (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: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).
% 0.21/0.44  
% 0.21/0.44  ********************************
% 0.21/0.44  *   All subproblems solved!    *
% 0.21/0.44  ********************************
% 0.21/0.44  % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.21/0.44  
% 0.21/0.44  %**** Beginning of derivation protocol ****
% 0.21/0.44  % SZS output start CNFRefutation
% See solution above
% 0.21/0.44  
% 0.21/0.44  %**** End of derivation protocol ****
% 0.21/0.44  %**** no. of clauses in derivation: 52 ****
% 0.21/0.44  %**** clause counter: 64 ****
% 0.21/0.44  
% 0.21/0.44  % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------