TSTP Solution File: MSC015-1.005 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : MSC015-1.005 : TPTP v8.1.0. Released v3.5.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n011.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 : Sun Jul 17 22:50:27 EDT 2022

% Result   : Unsatisfiable 0.13s 0.41s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   53 (  35 unt;   3 typ;   0 def)
%            Number of atoms       :  187 (  51 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  455 (  35   ~;  35   |;   0   &; 385   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   4 con; 0-5 aty)
%            Number of variables   :   80 (   0   ^  80   !;   0   ?;  80   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_p,type,
    p: $i > $i > $i > $i > $i > $o ).

thf(tp_s0,type,
    s0: $i ).

thf(tp_s1,type,
    s1: $i ).

thf(1,axiom,
    ( ~ ( p @ s0 @ s1 @ s1 @ s1 @ s1 )
    | ( p @ s1 @ s0 @ s0 @ s0 @ s0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5) ).

thf(2,axiom,
    ! [X0: $i] :
      ( ~ ( p @ X0 @ s0 @ s1 @ s1 @ s1 )
      | ( p @ X0 @ s1 @ s0 @ s0 @ s0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4) ).

thf(3,axiom,
    ! [X0: $i,X1: $i] :
      ( ~ ( p @ X0 @ X1 @ s0 @ s1 @ s1 )
      | ( p @ X0 @ X1 @ s1 @ s0 @ s0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3) ).

thf(4,axiom,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( p @ X0 @ X1 @ X2 @ s0 @ s1 )
      | ( p @ X0 @ X1 @ X2 @ s1 @ s0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2) ).

thf(5,axiom,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( p @ X0 @ X1 @ X2 @ X3 @ s0 )
      | ( p @ X0 @ X1 @ X2 @ X3 @ s1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1) ).

thf(6,axiom,
    p @ s0 @ s0 @ s0 @ s0 @ s0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',init) ).

thf(7,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(8,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[7]) ).

thf(9,negated_conjecture,
    ~ ( p @ s1 @ s1 @ s1 @ s1 @ s1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).

thf(10,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ( p @ s0 @ s1 @ s1 @ s1 @ s1 )
      | ( p @ s1 @ s0 @ s0 @ s0 @ s0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(12,plain,
    ( ( ! [X0: $i] :
          ( ~ ( p @ X0 @ s0 @ s1 @ s1 @ s1 )
          | ( p @ X0 @ s1 @ s0 @ s0 @ s0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(13,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ~ ( p @ X0 @ X1 @ s0 @ s1 @ s1 )
          | ( p @ X0 @ X1 @ s1 @ s0 @ s0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(14,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ~ ( p @ X0 @ X1 @ X2 @ s0 @ s1 )
          | ( p @ X0 @ X1 @ X2 @ s1 @ s0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(15,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
          ( ~ ( p @ X0 @ X1 @ X2 @ X3 @ s0 )
          | ( p @ X0 @ X1 @ X2 @ X3 @ s1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(16,plain,
    ( ( p @ s0 @ s0 @ s0 @ s0 @ s0 )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(17,plain,
    ( ( ~ ( p @ s1 @ s1 @ s1 @ s1 @ s1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(18,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(19,plain,
    ( ( ~ ( p @ s1 @ s1 @ s1 @ s1 @ s1 ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(20,plain,
    ( ( p @ s0 @ s0 @ s0 @ s0 @ s0 )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(21,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
          ( ~ ( p @ X0 @ X1 @ X2 @ X3 @ s0 )
          | ( p @ X0 @ X1 @ X2 @ X3 @ s1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(22,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ~ ( p @ X0 @ X1 @ X2 @ s0 @ s1 )
          | ( p @ X0 @ X1 @ X2 @ s1 @ s0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(23,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ~ ( p @ X0 @ X1 @ s0 @ s1 @ s1 )
          | ( p @ X0 @ X1 @ s1 @ s0 @ s0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(24,plain,
    ( ( ! [X0: $i] :
          ( ~ ( p @ X0 @ s0 @ s1 @ s1 @ s1 )
          | ( p @ X0 @ s1 @ s0 @ s0 @ s0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(25,plain,
    ( ( ~ ( p @ s0 @ s1 @ s1 @ s1 @ s1 )
      | ( p @ s1 @ s0 @ s0 @ s0 @ s0 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(26,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(27,plain,
    ( ( p @ s1 @ s1 @ s1 @ s1 @ s1 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(28,plain,
    ! [SV1: $i] :
      ( ( ! [SY10: $i,SY11: $i,SY12: $i] :
            ( ~ ( p @ SV1 @ SY10 @ SY11 @ SY12 @ s0 )
            | ( p @ SV1 @ SY10 @ SY11 @ SY12 @ s1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(29,plain,
    ! [SV2: $i] :
      ( ( ! [SY13: $i,SY14: $i] :
            ( ~ ( p @ SV2 @ SY13 @ SY14 @ s0 @ s1 )
            | ( p @ SV2 @ SY13 @ SY14 @ s1 @ s0 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(30,plain,
    ! [SV3: $i] :
      ( ( ! [SY15: $i] :
            ( ~ ( p @ SV3 @ SY15 @ s0 @ s1 @ s1 )
            | ( p @ SV3 @ SY15 @ s1 @ s0 @ s0 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(31,plain,
    ! [SV4: $i] :
      ( ( ~ ( p @ SV4 @ s0 @ s1 @ s1 @ s1 )
        | ( p @ SV4 @ s1 @ s0 @ s0 @ s0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(32,plain,
    ( ( ( ~ ( p @ s0 @ s1 @ s1 @ s1 @ s1 ) )
      = $true )
    | ( ( p @ s1 @ s0 @ s0 @ s0 @ s0 )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(33,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(34,plain,
    ! [SV5: $i,SV1: $i] :
      ( ( ! [SY16: $i,SY17: $i] :
            ( ~ ( p @ SV1 @ SV5 @ SY16 @ SY17 @ s0 )
            | ( p @ SV1 @ SV5 @ SY16 @ SY17 @ s1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV6: $i,SV2: $i] :
      ( ( ! [SY18: $i] :
            ( ~ ( p @ SV2 @ SV6 @ SY18 @ s0 @ s1 )
            | ( p @ SV2 @ SV6 @ SY18 @ s1 @ s0 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(36,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ~ ( p @ SV3 @ SV7 @ s0 @ s1 @ s1 )
        | ( p @ SV3 @ SV7 @ s1 @ s0 @ s0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(37,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( p @ SV4 @ s0 @ s1 @ s1 @ s1 ) )
        = $true )
      | ( ( p @ SV4 @ s1 @ s0 @ s0 @ s0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(38,plain,
    ( ( ( p @ s0 @ s1 @ s1 @ s1 @ s1 )
      = $false )
    | ( ( p @ s1 @ s0 @ s0 @ s0 @ s0 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV8: $i,SV5: $i,SV1: $i] :
      ( ( ! [SY19: $i] :
            ( ~ ( p @ SV1 @ SV5 @ SV8 @ SY19 @ s0 )
            | ( p @ SV1 @ SV5 @ SV8 @ SY19 @ s1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV9: $i,SV6: $i,SV2: $i] :
      ( ( ~ ( p @ SV2 @ SV6 @ SV9 @ s0 @ s1 )
        | ( p @ SV2 @ SV6 @ SV9 @ s1 @ s0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(41,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( ~ ( p @ SV3 @ SV7 @ s0 @ s1 @ s1 ) )
        = $true )
      | ( ( p @ SV3 @ SV7 @ s1 @ s0 @ s0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(42,plain,
    ! [SV4: $i] :
      ( ( ( p @ SV4 @ s0 @ s1 @ s1 @ s1 )
        = $false )
      | ( ( p @ SV4 @ s1 @ s0 @ s0 @ s0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(43,plain,
    ! [SV10: $i,SV8: $i,SV5: $i,SV1: $i] :
      ( ( ~ ( p @ SV1 @ SV5 @ SV8 @ SV10 @ s0 )
        | ( p @ SV1 @ SV5 @ SV8 @ SV10 @ s1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV9: $i,SV6: $i,SV2: $i] :
      ( ( ( ~ ( p @ SV2 @ SV6 @ SV9 @ s0 @ s1 ) )
        = $true )
      | ( ( p @ SV2 @ SV6 @ SV9 @ s1 @ s0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( p @ SV3 @ SV7 @ s0 @ s1 @ s1 )
        = $false )
      | ( ( p @ SV3 @ SV7 @ s1 @ s0 @ s0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV10: $i,SV8: $i,SV5: $i,SV1: $i] :
      ( ( ( ~ ( p @ SV1 @ SV5 @ SV8 @ SV10 @ s0 ) )
        = $true )
      | ( ( p @ SV1 @ SV5 @ SV8 @ SV10 @ s1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(47,plain,
    ! [SV9: $i,SV6: $i,SV2: $i] :
      ( ( ( p @ SV2 @ SV6 @ SV9 @ s0 @ s1 )
        = $false )
      | ( ( p @ SV2 @ SV6 @ SV9 @ s1 @ s0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(48,plain,
    ! [SV10: $i,SV8: $i,SV5: $i,SV1: $i] :
      ( ( ( p @ SV1 @ SV5 @ SV8 @ SV10 @ s0 )
        = $false )
      | ( ( p @ SV1 @ SV5 @ SV8 @ SV10 @ s1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(49,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[20,48,47,45,42,38,33,27]) ).

thf(50,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[49]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : MSC015-1.005 : TPTP v8.1.0. Released v3.5.0.
% 0.13/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 600
% 0.13/0.36  % DateTime : Fri Jul  1 16:04:34 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 7
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.37  (rf:0,axioms:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.13/0.41  
% 0.13/0.41  ********************************
% 0.13/0.41  *   All subproblems solved!    *
% 0.13/0.41  ********************************
% 0.13/0.41  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:49,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.41  
% 0.13/0.41  %**** Beginning of derivation protocol ****
% 0.13/0.41  % SZS output start CNFRefutation
% See solution above
% 0.13/0.41  
% 0.13/0.41  %**** End of derivation protocol ****
% 0.13/0.41  %**** no. of clauses in derivation: 50 ****
% 0.13/0.41  %**** clause counter: 49 ****
% 0.13/0.41  
% 0.13/0.41  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:49,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------