TSTP Solution File: SWV254-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n026.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 : Wed Jul 20 20:11:23 EDT 2022

% Result   : Unsatisfiable 0.22s 0.41s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   51 (  35 unt;   9 typ;   0 def)
%            Number of atoms       :  148 (  69 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  199 (  25   ~;  22   |;   0   &; 152   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   69 (   0   ^  69   !;   0   ?;  69   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_SetInterval_OatLeastLessThan,type,
    c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).

thf(tp_c_Suc,type,
    c_Suc: $i > $i ).

thf(tp_c_emptyset,type,
    c_emptyset: $i ).

thf(tp_c_insert,type,
    c_insert: $i > $i > $i > $i ).

thf(tp_c_lessequals,type,
    c_lessequals: $i > $i > $i > $o ).

thf(tp_class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

thf(tp_tc_nat,type,
    tc_nat: $i ).

thf(tp_v_nat,type,
    v_nat: $i ).

thf(tp_v_x,type,
    v_x: $i > $i ).

thf(1,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).

thf(2,axiom,
    ! [V_a: $i,V_A: $i,T_a: $i] :
      ( c_emptyset
     != ( c_insert @ V_a @ V_A @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).

thf(3,axiom,
    ! [V_m: $i] :
      ( ( c_SetInterval_OatLeastLessThan @ V_m @ ( c_Suc @ V_m ) @ tc_nat )
      = ( c_insert @ V_m @ c_emptyset @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).

thf(4,axiom,
    ! [T_a: $i,V_n: $i,V_m: $i] :
      ( ~ ( class_Orderings_Oorder @ T_a )
      | ~ ( c_lessequals @ V_n @ V_m @ T_a )
      | ( ( c_SetInterval_OatLeastLessThan @ V_m @ V_n @ T_a )
        = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).

thf(5,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(6,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[5]) ).

thf(7,negated_conjecture,
    ! [V_U: $i] :
      ( ( v_x @ V_U )
      = v_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(8,negated_conjecture,
    ! [V_U: $i] : ( c_lessequals @ V_U @ ( v_x @ V_U ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(9,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[6]) ).

thf(10,plain,
    ( ( class_Orderings_Oorder @ tc_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(11,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( c_emptyset
         != ( c_insert @ V_a @ V_A @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(12,plain,
    ( ( ! [V_m: $i] :
          ( ( c_SetInterval_OatLeastLessThan @ V_m @ ( c_Suc @ V_m ) @ tc_nat )
          = ( c_insert @ V_m @ c_emptyset @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(13,plain,
    ( ( ! [T_a: $i,V_n: $i,V_m: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ~ ( c_lessequals @ V_n @ V_m @ T_a )
          | ( ( c_SetInterval_OatLeastLessThan @ V_m @ V_n @ T_a )
            = c_emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(14,plain,
    ( ( ! [V_U: $i] :
          ( ( v_x @ V_U )
          = v_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(15,plain,
    ( ( ! [V_U: $i] : ( c_lessequals @ V_U @ ( v_x @ V_U ) @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(16,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(17,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( c_emptyset
         != ( c_insert @ V_a @ V_A @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(18,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_n: $i,V_m: $i] :
              ( ~ ( c_lessequals @ V_n @ V_m @ T_a )
              | ( ( c_SetInterval_OatLeastLessThan @ V_m @ V_n @ T_a )
                = c_emptyset ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(19,plain,
    ( ( ! [V_U: $i] : ( c_lessequals @ V_U @ ( v_x @ V_U ) @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ! [V_U: $i] :
          ( ( v_x @ V_U )
          = v_nat ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(21,plain,
    ( ( ! [T_a: $i] :
          ( ~ ( class_Orderings_Oorder @ T_a )
          | ! [V_n: $i,V_m: $i] :
              ( ~ ( c_lessequals @ V_n @ V_m @ T_a )
              | ( ( c_SetInterval_OatLeastLessThan @ V_m @ V_n @ T_a )
                = c_emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ! [V_m: $i] :
          ( ( c_SetInterval_OatLeastLessThan @ V_m @ ( c_Suc @ V_m ) @ tc_nat )
          = ( c_insert @ V_m @ c_emptyset @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(23,plain,
    ( ( ! [V_a: $i,V_A: $i,T_a: $i] :
          ( c_emptyset
         != ( c_insert @ V_a @ V_A @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(24,plain,
    ( ( class_Orderings_Oorder @ tc_nat )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(25,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(26,plain,
    ! [SV1: $i] :
      ( ( c_lessequals @ SV1 @ ( v_x @ SV1 ) @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(27,plain,
    ! [SV2: $i] :
      ( ( ( v_x @ SV2 )
        = v_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(28,plain,
    ! [SV3: $i] :
      ( ( ~ ( class_Orderings_Oorder @ SV3 )
        | ! [SY9: $i,SY10: $i] :
            ( ~ ( c_lessequals @ SY9 @ SY10 @ SV3 )
            | ( ( c_SetInterval_OatLeastLessThan @ SY10 @ SY9 @ SV3 )
              = c_emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(29,plain,
    ! [SV4: $i] :
      ( ( ( c_SetInterval_OatLeastLessThan @ SV4 @ ( c_Suc @ SV4 ) @ tc_nat )
        = ( c_insert @ SV4 @ c_emptyset @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(30,plain,
    ! [SV5: $i] :
      ( ( ! [SY11: $i,SY12: $i] :
            ( c_emptyset
           != ( c_insert @ SV5 @ SY11 @ SY12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(31,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(32,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( class_Orderings_Oorder @ SV3 ) )
        = $true )
      | ( ( ! [SY9: $i,SY10: $i] :
              ( ~ ( c_lessequals @ SY9 @ SY10 @ SV3 )
              | ( ( c_SetInterval_OatLeastLessThan @ SY10 @ SY9 @ SV3 )
                = c_emptyset ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV6: $i,SV5: $i] :
      ( ( ! [SY13: $i] :
            ( c_emptyset
           != ( c_insert @ SV5 @ SV6 @ SY13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV3: $i] :
      ( ( ( class_Orderings_Oorder @ SV3 )
        = $false )
      | ( ( ! [SY9: $i,SY10: $i] :
              ( ~ ( c_lessequals @ SY9 @ SY10 @ SV3 )
              | ( ( c_SetInterval_OatLeastLessThan @ SY10 @ SY9 @ SV3 )
                = c_emptyset ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(35,plain,
    ! [SV7: $i,SV6: $i,SV5: $i] :
      ( ( ( c_emptyset
         != ( c_insert @ SV5 @ SV6 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(36,plain,
    ! [SV3: $i,SV8: $i] :
      ( ( ( ! [SY14: $i] :
              ( ~ ( c_lessequals @ SV8 @ SY14 @ SV3 )
              | ( ( c_SetInterval_OatLeastLessThan @ SY14 @ SV8 @ SV3 )
                = c_emptyset ) ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV7: $i,SV6: $i,SV5: $i] :
      ( ( c_emptyset
        = ( c_insert @ SV5 @ SV6 @ SV7 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV3: $i,SV9: $i,SV8: $i] :
      ( ( ( ~ ( c_lessequals @ SV8 @ SV9 @ SV3 )
          | ( ( c_SetInterval_OatLeastLessThan @ SV9 @ SV8 @ SV3 )
            = c_emptyset ) )
        = $true )
      | ( ( class_Orderings_Oorder @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV3: $i,SV9: $i,SV8: $i] :
      ( ( ( ~ ( c_lessequals @ SV8 @ SV9 @ SV3 ) )
        = $true )
      | ( ( ( c_SetInterval_OatLeastLessThan @ SV9 @ SV8 @ SV3 )
          = c_emptyset )
        = $true )
      | ( ( class_Orderings_Oorder @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(40,plain,
    ! [SV3: $i,SV9: $i,SV8: $i] :
      ( ( ( c_lessequals @ SV8 @ SV9 @ SV3 )
        = $false )
      | ( ( ( c_SetInterval_OatLeastLessThan @ SV9 @ SV8 @ SV3 )
          = c_emptyset )
        = $true )
      | ( ( class_Orderings_Oorder @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(41,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[24,40,37,31,29,27,26]) ).

thf(42,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36  % Computer : n026.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 : Wed Jun 15 20:02:07 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.37  
% 0.15/0.37   No.of.Axioms: 6
% 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:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.22/0.41  
% 0.22/0.41  ********************************
% 0.22/0.41  *   All subproblems solved!    *
% 0.22/0.41  ********************************
% 0.22/0.41  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/0.41  
% 0.22/0.41  %**** Beginning of derivation protocol ****
% 0.22/0.41  % SZS output start CNFRefutation
% See solution above
% 0.22/0.41  
% 0.22/0.41  %**** End of derivation protocol ****
% 0.22/0.41  %**** no. of clauses in derivation: 42 ****
% 0.22/0.41  %**** clause counter: 41 ****
% 0.22/0.41  
% 0.22/0.41  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------