TSTP Solution File: SWV281-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SWV281-2 : 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 : n004.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 20:11:34 EDT 2022

% Result   : Unsatisfiable 0.14s 0.41s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   62 (  39 unt;  13 typ;   0 def)
%            Number of atoms       :  178 (  86 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  323 (  30   ~;  31   |;   0   &; 262   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   8 con; 0-3 aty)
%            Number of variables   :   95 (   0   ^  95   !;   0   ?;  95   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_0,type,
    c_0: $i ).

thf(tp_c_Event_Oused,type,
    c_Event_Oused: $i > $i ).

thf(tp_c_List_Olist_OCons,type,
    c_List_Olist_OCons: $i > $i > $i > $i ).

thf(tp_c_List_Olist_ONil,type,
    c_List_Olist_ONil: $i ).

thf(tp_c_Message_Omsg_ONonce,type,
    c_Message_Omsg_ONonce: $i > $i ).

thf(tp_c_in,type,
    c_in: $i > $i > $i > $o ).

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

thf(tp_c_plus,type,
    c_plus: $i > $i > $i > $i ).

thf(tp_tc_Message_Omsg,type,
    tc_Message_Omsg: $i ).

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

thf(tp_v_evs,type,
    v_evs: $i ).

thf(tp_v_evs_H,type,
    v_evs_H: $i ).

thf(tp_v_sko__urX,type,
    v_sko__urX: $i > $i ).

thf(1,axiom,
    ! [V_U: $i,V_evs: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ ( v_sko__urX @ V_evs ) @ V_U @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).

thf(2,axiom,
    ! [V_y: $i] :
      ( ( c_plus @ c_0 @ V_y @ tc_nat )
      = V_y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).

thf(3,axiom,
    ! [V_m: $i,V_k: $i,V_n: $i] :
      ( ( ( c_plus @ V_m @ V_k @ tc_nat )
       != ( c_plus @ V_n @ V_k @ tc_nat ) )
      | ( V_m = V_n ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).

thf(4,axiom,
    ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add2_0) ).

thf(5,axiom,
    ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
      ( c_List_Olist_ONil
     != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).

thf(6,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(7,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,negated_conjecture,
    ! [V_U: $i,V_V: $i] :
      ( ( V_U = V_V )
      | ( c_in @ ( c_Message_Omsg_ONonce @ V_V ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(9,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ! [V_U: $i,V_evs: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg )
          | ~ ( c_lessequals @ ( v_sko__urX @ V_evs ) @ V_U @ tc_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(11,plain,
    ( ( ! [V_y: $i] :
          ( ( c_plus @ c_0 @ V_y @ tc_nat )
          = V_y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(12,plain,
    ( ( ! [V_m: $i,V_k: $i,V_n: $i] :
          ( ( ( c_plus @ V_m @ V_k @ tc_nat )
           != ( c_plus @ V_n @ V_k @ tc_nat ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(13,plain,
    ( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(14,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( c_List_Olist_ONil
         != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(15,plain,
    ( ( ! [V_U: $i,V_V: $i] :
          ( ( V_U = V_V )
          | ( c_in @ ( c_Message_Omsg_ONonce @ V_V ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

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

thf(17,plain,
    ( ( ! [V_m: $i,V_k: $i,V_n: $i] :
          ( ( ( c_plus @ V_m @ V_k @ tc_nat )
           != ( c_plus @ V_n @ V_k @ tc_nat ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(18,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( c_List_Olist_ONil
         != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[14]) ).

thf(19,plain,
    ( ( ! [V_U: $i,V_V: $i] :
          ( ( V_U = V_V )
          | ( c_in @ ( c_Message_Omsg_ONonce @ V_V ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
          ( c_List_Olist_ONil
         != ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(22,plain,
    ( ( ! [V_m: $i,V_k: $i,V_n: $i] :
          ( ( ( c_plus @ V_m @ V_k @ tc_nat )
           != ( c_plus @ V_n @ V_k @ tc_nat ) )
          | ( V_m = V_n ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(23,plain,
    ( ( ! [V_y: $i] :
          ( ( c_plus @ c_0 @ V_y @ tc_nat )
          = V_y ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(24,plain,
    ( ( ! [V_U: $i,V_evs: $i] :
          ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg )
          | ~ ( c_lessequals @ ( v_sko__urX @ V_evs ) @ V_U @ tc_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

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

thf(26,plain,
    ! [SV1: $i] :
      ( ( ! [SY13: $i] :
            ( ( SV1 = SY13 )
            | ( c_in @ ( c_Message_Omsg_ONonce @ SY13 ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
            | ( c_in @ ( c_Message_Omsg_ONonce @ SV1 ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(27,plain,
    ! [SV2: $i] :
      ( ( ! [SY14: $i,SY15: $i] :
            ( c_List_Olist_ONil
           != ( c_List_Olist_OCons @ SV2 @ SY14 @ SY15 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(28,plain,
    ! [SV3: $i] :
      ( ( ! [SY16: $i] : ( c_lessequals @ SV3 @ ( c_plus @ SY16 @ SV3 @ tc_nat ) @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(29,plain,
    ! [SV4: $i] :
      ( ( ! [SY17: $i,SY18: $i] :
            ( ( ( c_plus @ SV4 @ SY17 @ tc_nat )
             != ( c_plus @ SY18 @ SY17 @ tc_nat ) )
            | ( SV4 = SY18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(30,plain,
    ! [SV5: $i] :
      ( ( ( c_plus @ c_0 @ SV5 @ tc_nat )
        = SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(31,plain,
    ! [SV6: $i] :
      ( ( ! [SY19: $i] :
            ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV6 ) @ ( c_Event_Oused @ SY19 ) @ tc_Message_Omsg )
            | ~ ( c_lessequals @ ( v_sko__urX @ SY19 ) @ SV6 @ tc_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(32,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(33,plain,
    ! [SV7: $i,SV1: $i] :
      ( ( ( SV1 = SV7 )
        | ( c_in @ ( c_Message_Omsg_ONonce @ SV7 ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
        | ( c_in @ ( c_Message_Omsg_ONonce @ SV1 ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(34,plain,
    ! [SV8: $i,SV2: $i] :
      ( ( ! [SY20: $i] :
            ( c_List_Olist_ONil
           != ( c_List_Olist_OCons @ SV2 @ SV8 @ SY20 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(35,plain,
    ! [SV9: $i,SV3: $i] :
      ( ( c_lessequals @ SV3 @ ( c_plus @ SV9 @ SV3 @ tc_nat ) @ tc_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(36,plain,
    ! [SV10: $i,SV4: $i] :
      ( ( ! [SY21: $i] :
            ( ( ( c_plus @ SV4 @ SV10 @ tc_nat )
             != ( c_plus @ SY21 @ SV10 @ tc_nat ) )
            | ( SV4 = SY21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(37,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV6 ) @ ( c_Event_Oused @ SV11 ) @ tc_Message_Omsg )
        | ~ ( c_lessequals @ ( v_sko__urX @ SV11 ) @ SV6 @ tc_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(38,plain,
    ! [SV7: $i,SV1: $i] :
      ( ( ( SV1 = SV7 )
        = $true )
      | ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV7 ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
          | ( c_in @ ( c_Message_Omsg_ONonce @ SV1 ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(39,plain,
    ! [SV12: $i,SV8: $i,SV2: $i] :
      ( ( ( c_List_Olist_ONil
         != ( c_List_Olist_OCons @ SV2 @ SV8 @ SV12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV13: $i,SV10: $i,SV4: $i] :
      ( ( ( ( c_plus @ SV4 @ SV10 @ tc_nat )
         != ( c_plus @ SV13 @ SV10 @ tc_nat ) )
        | ( SV4 = SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(41,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV6 ) @ ( c_Event_Oused @ SV11 ) @ tc_Message_Omsg ) )
        = $true )
      | ( ( ~ ( c_lessequals @ ( v_sko__urX @ SV11 ) @ SV6 @ tc_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(42,plain,
    ! [SV1: $i,SV7: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV7 ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
        = $true )
      | ( ( c_in @ ( c_Message_Omsg_ONonce @ SV1 ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg )
        = $true )
      | ( ( SV1 = SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV12: $i,SV8: $i,SV2: $i] :
      ( ( c_List_Olist_ONil
        = ( c_List_Olist_OCons @ SV2 @ SV8 @ SV12 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV13: $i,SV10: $i,SV4: $i] :
      ( ( ( ( ( c_plus @ SV4 @ SV10 @ tc_nat )
           != ( c_plus @ SV13 @ SV10 @ tc_nat ) ) )
        = $true )
      | ( ( SV4 = SV13 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV6 ) @ ( c_Event_Oused @ SV11 ) @ tc_Message_Omsg )
        = $false )
      | ( ( ~ ( c_lessequals @ ( v_sko__urX @ SV11 ) @ SV6 @ tc_nat ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV13: $i,SV10: $i,SV4: $i] :
      ( ( ( ( c_plus @ SV4 @ SV10 @ tc_nat )
          = ( c_plus @ SV13 @ SV10 @ tc_nat ) )
        = $false )
      | ( ( SV4 = SV13 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(47,plain,
    ! [SV6: $i,SV11: $i] :
      ( ( ( c_lessequals @ ( v_sko__urX @ SV11 ) @ SV6 @ tc_nat )
        = $false )
      | ( ( c_in @ ( c_Message_Omsg_ONonce @ SV6 ) @ ( c_Event_Oused @ SV11 ) @ tc_Message_Omsg )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(48,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[30,47,46,43,42,35,32]) ).

thf(49,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV281-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Wed Jun 15 05:35:24 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  
% 0.14/0.36   No.of.Axioms: 6
% 0.14/0.36  
% 0.14/0.36   Length.of.Defs: 0
% 0.14/0.36  
% 0.14/0.36   Contains.Choice.Funs: false
% 0.14/0.36  (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)..
% 0.14/0.41  
% 0.14/0.41  ********************************
% 0.14/0.41  *   All subproblems solved!    *
% 0.14/0.41  ********************************
% 0.14/0.41  % 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:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.41  
% 0.14/0.41  %**** Beginning of derivation protocol ****
% 0.14/0.41  % SZS output start CNFRefutation
% See solution above
% 0.14/0.41  
% 0.14/0.41  %**** End of derivation protocol ****
% 0.14/0.41  %**** no. of clauses in derivation: 49 ****
% 0.14/0.41  %**** clause counter: 48 ****
% 0.14/0.41  
% 0.14/0.41  % 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:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------