TSTP Solution File: NUM730^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM730^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n009.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 : Mon Jul 18 11:54:46 EDT 2022

% Result   : Theorem 0.40s 0.62s
% Output   : CNFRefutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   27 (  13 unt;  12 typ;   0 def)
%            Number of atoms       :   83 (  27 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  268 (   2   ~;   0   |;   0   &; 266   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   14 (   0   ^  14   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_frac,type,
    frac: $tType ).

thf(tp_nat,type,
    nat: $tType ).

thf(tp_c1x,type,
    c1x: frac > nat ).

thf(tp_c1y,type,
    c1y: frac > nat ).

thf(tp_c2x,type,
    c2x: frac > nat ).

thf(tp_c2y,type,
    c2y: frac > nat ).

thf(tp_less,type,
    less: nat > nat > $o ).

thf(tp_more,type,
    more: nat > nat > $o ).

thf(tp_orec3,type,
    orec3: $o > $o > $o > $o ).

thf(tp_ts,type,
    ts: nat > nat > nat ).

thf(tp_x,type,
    x: frac ).

thf(tp_y,type,
    y: frac ).

thf(1,axiom,
    ! [Xx: nat,Xy: nat] : ( orec3 @ ( Xx = Xy ) @ ( more @ Xx @ Xy ) @ ( less @ Xx @ Xy ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10) ).

thf(2,conjecture,
    ( orec3
    @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
      = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
    @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
    @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41) ).

thf(3,negated_conjecture,
    ( ( orec3
      @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
        = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[2]) ).

thf(4,plain,
    ( ( orec3
      @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
        = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: nat,Xy: nat] : ( orec3 @ ( Xx = Xy ) @ ( more @ Xx @ Xy ) @ ( less @ Xx @ Xy ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(6,plain,
    ( ( ~ ( orec3
          @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
            = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
          @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
          @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ! [Xx: nat,Xy: nat] : ( orec3 @ ( Xx = Xy ) @ ( more @ Xx @ Xy ) @ ( less @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ~ ( orec3
          @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
            = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
          @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
          @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(9,plain,
    ! [SV1: nat] :
      ( ( ! [SY2: nat] : ( orec3 @ ( SV1 = SY2 ) @ ( more @ SV1 @ SY2 ) @ ( less @ SV1 @ SY2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7]) ).

thf(10,plain,
    ( ( orec3
      @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
        = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[8]) ).

thf(11,plain,
    ! [SV2: nat,SV1: nat] :
      ( ( orec3 @ ( SV1 = SV2 ) @ ( more @ SV1 @ SV2 ) @ ( less @ SV1 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[9]) ).

thf(12,plain,
    ! [SV3: nat,SV4: nat] :
      ( ( orec3 @ ( SV4 = SV3 ) @ ( more @ SV4 @ SV3 ) @ ( less @ SV4 @ SV3 ) )
      = $true ),
    inference(rename,[status(thm)],[11]) ).

thf(13,plain,
    ! [SV3: nat,SV4: nat] :
      ( ( ( orec3 @ ( SV4 = SV3 ) @ ( more @ SV4 @ SV3 ) @ ( less @ SV4 @ SV3 ) )
        = ( orec3
          @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
            = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
          @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
          @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) )
      = $false ),
    inference(res,[status(thm)],[12,10]) ).

thf(50,plain,
    $false = $true,
    inference(extuni,[status(esa)],[13:[bind(SV3,$thf( ts @ ( c1y @ y ) @ ( c2x @ x ) )),bind(SV4,$thf( ts @ ( c1x @ x ) @ ( c2y @ y ) ))]]) ).

thf(51,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM730^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n009.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 : Thu Jul  7 00:37:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 1
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.40/0.62  
% 0.40/0.62  ********************************
% 0.40/0.62  *   All subproblems solved!    *
% 0.40/0.62  ********************************
% 0.40/0.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:50,loop_count:2,foatp_calls:1,translation:fof_full)
% 0.40/0.62  
% 0.40/0.62  %**** Beginning of derivation protocol ****
% 0.40/0.62  % SZS output start CNFRefutation
% See solution above
% 0.40/0.62  
% 0.40/0.62  %**** End of derivation protocol ****
% 0.40/0.62  %**** no. of clauses in derivation: 15 ****
% 0.40/0.62  %**** clause counter: 50 ****
% 0.40/0.62  
% 0.40/0.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:50,loop_count:2,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------