TSTP Solution File: LAT271-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LAT271-2 : 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 : Sun Jul 17 05:45:24 EDT 2022

% Result   : Unsatisfiable 0.20s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   44 (  25 unt;  12 typ;   0 def)
%            Number of atoms       :  130 (  35 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  404 (  27   ~;  28   |;   0   &; 349   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   8 con; 0-4 aty)
%            Number of variables   :   84 (   0   ^  84   !;   0   ?;  84   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(tp_c_Tarski_Ointerval,type,
    c_Tarski_Ointerval: $i > $i > $i > $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_t_a,type,
    t_a: $i ).

thf(tp_tc_prod,type,
    tc_prod: $i > $i > $i ).

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

thf(tp_v_S,type,
    v_S: $i ).

thf(tp_v_a,type,
    v_a: $i ).

thf(tp_v_b,type,
    v_b: $i ).

thf(tp_v_r,type,
    v_r: $i ).

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

thf(1,axiom,
    ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
      ( ~ ( c_in @ V_x @ V_S @ T_a )
      | ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
      | ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_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,
    ~ ( c_in @ ( c_Pair @ v_a @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).

thf(5,negated_conjecture,
    c_in @ v_x @ v_S @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(6,negated_conjecture,
    c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( 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_x: $i,V_S: $i,T_a: $i,V_r: $i,V_a: $i,V_b: $i] :
          ( ~ ( c_in @ V_x @ V_S @ T_a )
          | ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
          | ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(9,plain,
    ( ( ~ ( c_in @ ( c_Pair @ v_a @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(10,plain,
    ( ( c_in @ v_x @ v_S @ t_a )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(11,plain,
    ( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( 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_x: $i,V_S: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ V_x @ V_S @ T_a )
          | ! [V_a: $i] :
              ( ! [V_b: $i] :
                  ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(14,plain,
    ( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(15,plain,
    ( ( c_in @ v_x @ v_S @ t_a )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(16,plain,
    ( ( ~ ( c_in @ ( c_Pair @ v_a @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(17,plain,
    ( ( ! [V_x: $i,V_S: $i,T_a: $i,V_r: $i] :
          ( ~ ( c_in @ V_x @ V_S @ T_a )
          | ! [V_a: $i] :
              ( ! [V_b: $i] :
                  ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ V_r @ V_a @ V_b @ T_a ) @ ( tc_set @ T_a ) )
              | ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

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

thf(19,plain,
    ( ( c_in @ ( c_Pair @ v_a @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV1: $i] :
      ( ( ! [SY6: $i,SY7: $i,SY8: $i] :
            ( ~ ( c_in @ SV1 @ SY6 @ SY7 )
            | ! [SY9: $i] :
                ( ! [V_b: $i] :
                    ~ ( c_lessequals @ SY6 @ ( c_Tarski_Ointerval @ SY8 @ SY9 @ V_b @ SY7 ) @ ( tc_set @ SY7 ) )
                | ( c_in @ ( c_Pair @ SY9 @ SV1 @ SY7 @ SY7 ) @ SY8 @ ( tc_prod @ SY7 @ SY7 ) ) ) ) )
      = $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] :
      ( ( ! [SY11: $i,SY12: $i] :
            ( ~ ( c_in @ SV1 @ SV2 @ SY11 )
            | ! [SY13: $i] :
                ( ! [SY14: $i] :
                    ~ ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SY12 @ SY13 @ SY14 @ SY11 ) @ ( tc_set @ SY11 ) )
                | ( c_in @ ( c_Pair @ SY13 @ SV1 @ SY11 @ SY11 ) @ SY12 @ ( tc_prod @ SY11 @ SY11 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV3: $i,SV2: $i,SV1: $i] :
      ( ( ! [SY15: $i] :
            ( ~ ( c_in @ SV1 @ SV2 @ SV3 )
            | ! [SY16: $i] :
                ( ! [SY17: $i] :
                    ~ ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SY15 @ SY16 @ SY17 @ SV3 ) @ ( tc_set @ SV3 ) )
                | ( c_in @ ( c_Pair @ SY16 @ SV1 @ SV3 @ SV3 ) @ SY15 @ ( tc_prod @ SV3 @ SV3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(24,plain,
    ! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
      ( ( ~ ( c_in @ SV1 @ SV2 @ SV3 )
        | ! [SY18: $i] :
            ( ! [SY19: $i] :
                ~ ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SV4 @ SY18 @ SY19 @ SV3 ) @ ( tc_set @ SV3 ) )
            | ( c_in @ ( c_Pair @ SY18 @ SV1 @ SV3 @ SV3 ) @ SV4 @ ( tc_prod @ SV3 @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(25,plain,
    ! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
      ( ( ( ~ ( c_in @ SV1 @ SV2 @ SV3 ) )
        = $true )
      | ( ( ! [SY18: $i] :
              ( ! [SY19: $i] :
                  ~ ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SV4 @ SY18 @ SY19 @ SV3 ) @ ( tc_set @ SV3 ) )
              | ( c_in @ ( c_Pair @ SY18 @ SV1 @ SV3 @ SV3 ) @ SV4 @ ( tc_prod @ SV3 @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(26,plain,
    ! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
      ( ( ( c_in @ SV1 @ SV2 @ SV3 )
        = $false )
      | ( ( ! [SY18: $i] :
              ( ! [SY19: $i] :
                  ~ ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SV4 @ SY18 @ SY19 @ SV3 ) @ ( tc_set @ SV3 ) )
              | ( c_in @ ( c_Pair @ SY18 @ SV1 @ SV3 @ SV3 ) @ SV4 @ ( tc_prod @ SV3 @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(27,plain,
    ! [SV1: $i,SV3: $i,SV5: $i,SV4: $i,SV2: $i] :
      ( ( ( ! [SY20: $i] :
              ~ ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SV4 @ SV5 @ SY20 @ SV3 ) @ ( tc_set @ SV3 ) )
          | ( c_in @ ( c_Pair @ SV5 @ SV1 @ SV3 @ SV3 ) @ SV4 @ ( tc_prod @ SV3 @ SV3 ) ) )
        = $true )
      | ( ( c_in @ SV1 @ SV2 @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(28,plain,
    ! [SV1: $i,SV3: $i,SV5: $i,SV4: $i,SV2: $i] :
      ( ( ( ! [SY20: $i] :
              ~ ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SV4 @ SV5 @ SY20 @ SV3 ) @ ( tc_set @ SV3 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV5 @ SV1 @ SV3 @ SV3 ) @ SV4 @ ( tc_prod @ SV3 @ SV3 ) )
        = $true )
      | ( ( c_in @ SV1 @ SV2 @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(29,plain,
    ! [SV1: $i,SV3: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
      ( ( ( ~ ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SV4 @ SV5 @ SV6 @ SV3 ) @ ( tc_set @ SV3 ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV5 @ SV1 @ SV3 @ SV3 ) @ SV4 @ ( tc_prod @ SV3 @ SV3 ) )
        = $true )
      | ( ( c_in @ SV1 @ SV2 @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(30,plain,
    ! [SV1: $i,SV3: $i,SV6: $i,SV5: $i,SV4: $i,SV2: $i] :
      ( ( ( c_lessequals @ SV2 @ ( c_Tarski_Ointerval @ SV4 @ SV5 @ SV6 @ SV3 ) @ ( tc_set @ SV3 ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV5 @ SV1 @ SV3 @ SV3 ) @ SV4 @ ( tc_prod @ SV3 @ SV3 ) )
        = $true )
      | ( ( c_in @ SV1 @ SV2 @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(31,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[14,30,21,19,15]) ).

thf(32,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT271-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jun 29 18:20:18 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 4
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (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).
% 0.20/0.39  
% 0.20/0.39  ********************************
% 0.20/0.39  *   All subproblems solved!    *
% 0.20/0.39  ********************************
% 0.20/0.39  % 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:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.40  
% 0.20/0.40  %**** Beginning of derivation protocol ****
% 0.20/0.40  % SZS output start CNFRefutation
% See solution above
% 0.20/0.40  
% 0.20/0.40  %**** End of derivation protocol ****
% 0.20/0.40  %**** no. of clauses in derivation: 32 ****
% 0.20/0.40  %**** clause counter: 31 ****
% 0.20/0.40  
% 0.20/0.40  % 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:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------