TSTP Solution File: SWV048+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWV048+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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  : 300s
% DateTime : Tue May 21 05:50:23 EDT 2024

% Result   : Theorem 166.14s 29.78s
% Output   : Refutation 166.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   62 (  29 unt;  21 typ;   0 def)
%            Number of atoms       :   87 (  53 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  405 (  35   ~;  19   |;  18   &; 324   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  21 usr;  15 con; 0-3 aty)
%            Number of variables   :   15 (   0   ^  15   !;   0   ?;  15   :)

% Comments : 
%------------------------------------------------------------------------------
thf(pv78_type,type,
    pv78: $i ).

thf(sum_type,type,
    sum: $i > $i > $i > $i ).

thf(n0_type,type,
    n0: $i ).

thf(minus_type,type,
    minus: $i > $i > $i ).

thf(n135300_type,type,
    n135300: $i ).

thf(n1_type,type,
    n1: $i ).

thf(a_select3_type,type,
    a_select3: $i > $i > $i > $i ).

thf(q_type,type,
    q: $i ).

thf(pv79_type,type,
    pv79: $i ).

thf(pv35_type,type,
    pv35: $i ).

thf(leq_type,type,
    leq: $i > $i > $o ).

thf(n5_type,type,
    n5: $i ).

thf(times_type,type,
    times: $i > $i > $i ).

thf(pv81_type,type,
    pv81: $i ).

thf(a_select2_type,type,
    a_select2: $i > $i > $i ).

thf(x_type,type,
    x: $i ).

thf(true_type,type,
    true: $o ).

thf(succ_type,type,
    succ: $i > $i ).

thf(pred_type,type,
    pred: $i > $i ).

thf(tptp_minus_1_type,type,
    tptp_minus_1: $i ).

thf(sk1_type,type,
    sk1: $o ).

thf(31,axiom,
    ! [A: $i] :
      ( ( sum @ n0 @ tptp_minus_1 @ A )
      = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).

thf(173,plain,
    ! [A: $i] :
      ( ( sum @ n0 @ tptp_minus_1 @ A )
      = n0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(174,plain,
    ! [A: $i] :
      ( ( sum @ n0 @ tptp_minus_1 @ A )
      = n0 ),
    inference(cnf,[status(esa)],[173]) ).

thf(175,plain,
    ! [A: $i] :
      ( ( sum @ n0 @ tptp_minus_1 @ A )
      = n0 ),
    inference(lifteq,[status(thm)],[174]) ).

thf(1,conjecture,
    ( ( ( pv78
        = ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
      & ( leq @ n0 @ pv35 )
      & ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) )
   => ( ( ( n0 != pv78 )
       => ( ( n0
            = ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) )
          & ( pv78
            = ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
          & ( leq @ n0 @ pv35 )
          & ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) ) )
      & ( ( n0 = pv78 )
       => true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0016) ).

thf(2,negated_conjecture,
    ~ ( ( ( pv78
          = ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
        & ( leq @ n0 @ pv35 )
        & ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) )
     => ( ( ( n0 != pv78 )
         => ( ( n0
              = ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) )
            & ( pv78
              = ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
            & ( leq @ n0 @ pv35 )
            & ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) ) )
        & ( ( n0 = pv78 )
         => true ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(93,plain,
    ~ ( ( ( pv78
          = ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
        & ( leq @ n0 @ pv35 )
        & ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) )
     => ( ( ( n0 != pv78 )
         => ( ( n0
              = ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) )
            & ( pv78
              = ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
            & ( leq @ n0 @ pv35 )
            & ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) ) )
        & ( ( n0 = pv78 )
         => true ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(98,plain,
    ( ( n0
     != ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) )
    | ( pv78
     != ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
    | ~ ( leq @ n0 @ pv35 )
    | ~ ( leq @ pv35 @ ( minus @ n5 @ n1 ) )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[93]) ).

thf(102,plain,
    ( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
     != n0 )
    | ( ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) )
     != pv78 )
    | ~ ( leq @ n0 @ pv35 )
    | ~ ( leq @ pv35 @ ( minus @ n5 @ n1 ) )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[98]) ).

thf(100,plain,
    leq @ n0 @ pv35,
    inference(cnf,[status(esa)],[93]) ).

thf(96,plain,
    ( sk1
    | ~ true ),
    inference(cnf,[status(esa)],[93]) ).

thf(44,axiom,
    true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ttrue) ).

thf(321,plain,
    true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(565,plain,
    ( sk1
    | ~ $true ),
    inference(rewrite,[status(thm)],[96,321]) ).

thf(566,plain,
    sk1,
    inference(simp,[status(thm)],[565]) ).

thf(95,plain,
    leq @ pv35 @ ( minus @ n5 @ n1 ),
    inference(cnf,[status(esa)],[93]) ).

thf(572,plain,
    ( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
     != n0 )
    | ( ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) )
     != pv78 )
    | ~ $true
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[102,100,566,95]) ).

thf(573,plain,
    ( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
     != n0 )
    | ( ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) )
     != pv78 ) ),
    inference(simp,[status(thm)],[572]) ).

thf(94,plain,
    ( pv78
    = ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) ),
    inference(cnf,[status(esa)],[93]) ).

thf(104,plain,
    ( ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) )
    = pv78 ),
    inference(lifteq,[status(thm)],[94]) ).

thf(698,plain,
    ( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
     != n0 )
    | ( pv78 != pv78 ) ),
    inference(rewrite,[status(thm)],[573,104]) ).

thf(699,plain,
    ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
   != n0 ),
    inference(simp,[status(thm)],[698]) ).

thf(8209,plain,
    ! [A: $i] :
      ( ( sum @ n0 @ tptp_minus_1 @ A )
     != ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[175,699]) ).

thf(8237,plain,
    ! [A: $i] :
      ( ( n0 != n0 )
      | ( ( minus @ n0 @ n1 )
       != tptp_minus_1 )
      | ( A
       != ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) ),
    inference(simp,[status(thm)],[8209]) ).

thf(8268,plain,
    ( ( minus @ n0 @ n1 )
   != tptp_minus_1 ),
    inference(simp,[status(thm)],[8237]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( minus @ A @ n1 )
      = ( pred @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).

thf(222,plain,
    ! [A: $i] :
      ( ( minus @ A @ n1 )
      = ( pred @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(223,plain,
    ! [A: $i] :
      ( ( minus @ A @ n1 )
      = ( pred @ A ) ),
    inference(cnf,[status(esa)],[222]) ).

thf(224,plain,
    ! [A: $i] :
      ( ( minus @ A @ n1 )
      = ( pred @ A ) ),
    inference(lifteq,[status(thm)],[223]) ).

thf(23513,plain,
    ( ( pred @ n0 )
   != tptp_minus_1 ),
    inference(rewrite,[status(thm)],[8268,224]) ).

thf(49,axiom,
    ( ( succ @ tptp_minus_1 )
    = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).

thf(330,plain,
    ( ( succ @ tptp_minus_1 )
    = n0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(331,plain,
    ( ( succ @ tptp_minus_1 )
    = n0 ),
    inference(lifteq,[status(thm)],[330]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( pred @ ( succ @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).

thf(127,plain,
    ! [A: $i] :
      ( ( pred @ ( succ @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(128,plain,
    ! [A: $i] :
      ( ( pred @ ( succ @ A ) )
      = A ),
    inference(cnf,[status(esa)],[127]) ).

thf(129,plain,
    ! [A: $i] :
      ( ( pred @ ( succ @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[128]) ).

thf(3754,plain,
    ! [A: $i] :
      ( ( ( pred @ n0 )
        = A )
      | ( ( succ @ tptp_minus_1 )
       != ( succ @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[331,129]) ).

thf(3755,plain,
    ( ( pred @ n0 )
    = tptp_minus_1 ),
    inference(pattern_uni,[status(thm)],[3754:[bind(A,$thf( tptp_minus_1 ))]]) ).

thf(23527,plain,
    tptp_minus_1 != tptp_minus_1,
    inference(rewrite,[status(thm)],[23513,3755]) ).

thf(23528,plain,
    $false,
    inference(simp,[status(thm)],[23527]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWV048+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun May 19 09:03:24 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.17/1.09  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.78/1.35  % [INFO] 	 Parsing done (254ms). 
% 1.78/1.36  % [INFO] 	 Running in sequential loop mode. 
% 2.54/1.80  % [INFO] 	 nitpick registered as external prover. 
% 2.54/1.81  % [INFO] 	 Scanning for conjecture ... 
% 2.82/1.95  % [INFO] 	 Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ... 
% 3.16/2.07  % [INFO] 	 Axiom selection finished. Selected 90 axioms (removed 1 axioms). 
% 3.61/2.22  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.61/2.25  % [INFO] 	 Type checking passed. 
% 3.61/2.25  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 166.14/29.77  % [INFO] 	 Killing All external provers ... 
% 166.14/29.77  % Time passed: 29255ms (effective reasoning time: 28403ms)
% 166.14/29.77  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 166.14/29.78  % Axioms used in derivation (5): pred_minus_1, ttrue, succ_tptp_minus_1, sum_plus_base, pred_succ
% 166.14/29.78  % No. of inferences in proof: 41
% 166.14/29.78  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29255 ms resp. 28403 ms w/o parsing
% 166.14/29.82  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 166.14/29.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------