TSTP Solution File: SET855-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET855-2 : 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 : Tue Jul 19 03:05:43 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   35 (  24 unt;   6 typ;   0 def)
%            Number of atoms       :  107 (  44 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  185 (  22   ~;  20   |;   0   &; 143   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-3 aty)
%            Number of variables   :   30 (   0   ^  30   !;   0   ?;  30   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_Union,type,
    c_Union: $i > $i > $i ).

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

thf(tp_t_a,type,
    t_a: $i ).

thf(tp_tc_set,type,
    tc_set: $i > $i ).

thf(tp_v_Y,type,
    v_Y: $i ).

thf(tp_v_n,type,
    v_n: $i ).

thf(1,axiom,
    ! [V_B: $i,V_A: $i,T_a: $i] :
      ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
      | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ( V_A = V_B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).

thf(2,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(3,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[2]) ).

thf(4,negated_conjecture,
    v_n
 != ( c_Union @ v_Y @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(5,negated_conjecture,
    c_lessequals @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ v_n @ ( tc_set @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(6,negated_conjecture,
    c_lessequals @ v_n @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(7,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ! [V_B: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
          | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( V_A = V_B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(9,plain,
    ( ( ( v_n
       != ( c_Union @ v_Y @ ( tc_set @ t_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(10,plain,
    ( ( c_lessequals @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(11,plain,
    ( ( c_lessequals @ v_n @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(12,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(13,plain,
    ( ( ( v_n
       != ( c_Union @ v_Y @ ( tc_set @ t_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(14,plain,
    ( ( c_lessequals @ v_n @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(15,plain,
    ( ( c_lessequals @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(16,plain,
    ( ( ( v_n
       != ( c_Union @ v_Y @ ( tc_set @ t_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ! [V_B: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
          | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( V_A = V_B ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(18,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(19,plain,
    ( ( v_n
      = ( c_Union @ v_Y @ ( tc_set @ t_a ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV1: $i] :
      ( ( ! [SY3: $i,SY4: $i] :
            ( ~ ( c_lessequals @ SV1 @ SY3 @ ( tc_set @ SY4 ) )
            | ~ ( c_lessequals @ SY3 @ SV1 @ ( tc_set @ SY4 ) )
            | ( SY3 = SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(21,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ! [SY5: $i] :
            ( ~ ( c_lessequals @ SV1 @ SV2 @ ( tc_set @ SY5 ) )
            | ~ ( c_lessequals @ SV2 @ SV1 @ ( tc_set @ SY5 ) )
            | ( SV2 = SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV3: $i,SV2: $i,SV1: $i] :
      ( ( ~ ( c_lessequals @ SV1 @ SV2 @ ( tc_set @ SV3 ) )
        | ~ ( c_lessequals @ SV2 @ SV1 @ ( tc_set @ SV3 ) )
        | ( SV2 = SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(24,plain,
    ! [SV3: $i,SV2: $i,SV1: $i] :
      ( ( ( ~ ( c_lessequals @ SV1 @ SV2 @ ( tc_set @ SV3 ) ) )
        = $true )
      | ( ( ~ ( c_lessequals @ SV2 @ SV1 @ ( tc_set @ SV3 ) )
          | ( SV2 = SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(25,plain,
    ! [SV3: $i,SV2: $i,SV1: $i] :
      ( ( ( c_lessequals @ SV1 @ SV2 @ ( tc_set @ SV3 ) )
        = $false )
      | ( ( ~ ( c_lessequals @ SV2 @ SV1 @ ( tc_set @ SV3 ) )
          | ( SV2 = SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(26,plain,
    ! [SV3: $i,SV1: $i,SV2: $i] :
      ( ( ( ~ ( c_lessequals @ SV2 @ SV1 @ ( tc_set @ SV3 ) ) )
        = $true )
      | ( ( SV2 = SV1 )
        = $true )
      | ( ( c_lessequals @ SV1 @ SV2 @ ( tc_set @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(27,plain,
    ! [SV3: $i,SV1: $i,SV2: $i] :
      ( ( ( c_lessequals @ SV2 @ SV1 @ ( tc_set @ SV3 ) )
        = $false )
      | ( ( SV2 = SV1 )
        = $true )
      | ( ( c_lessequals @ SV1 @ SV2 @ ( tc_set @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(28,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[14,27,21,19,15]) ).

thf(29,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : SET855-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n026.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 10:58:56 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 4
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.36  (rf:0,axioms:4,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:6,loop_count:0,foatp_calls:0,translation:fof_full)
% 0.13/0.39  ********************************
% 0.13/0.39  *   All subproblems solved!    *
% 0.13/0.39  ********************************
% 0.13/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:28,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39  
% 0.13/0.39  %**** Beginning of derivation protocol ****
% 0.13/0.39  % SZS output start CNFRefutation
% See solution above
% 0.13/0.39  
% 0.13/0.39  %**** End of derivation protocol ****
% 0.13/0.39  %**** no. of clauses in derivation: 29 ****
% 0.13/0.39  %**** clause counter: 28 ****
% 0.13/0.39  
% 0.13/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:28,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------