TSTP Solution File: SWC255+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC255+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 04:34:38 EDT 2024

% Result   : Theorem 5.73s 2.46s
% Output   : Refutation 5.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   28 (   7 unt;   9 typ;   0 def)
%            Number of atoms       :   60 (  11 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  118 (  28   ~;  24   |;   3   &;  51   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   12 (   0   ^  12   !;   0   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ssList_type,type,
    ssList: $i > $o ).

thf(neq_type,type,
    neq: $i > $i > $o ).

thf(nil_type,type,
    nil: $i ).

thf(singletonP_type,type,
    singletonP: $i > $o ).

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

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $o ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( B != D )
                    | ( A != C )
                    | ( ( ~ ( neq @ B @ nil )
                        | ~ ( singletonP @ C )
                        | ( singletonP @ A ) )
                      & ( ~ ( neq @ B @ nil )
                        | ( neq @ D @ nil ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ssList @ A )
       => ! [B: $i] :
            ( ( ssList @ B )
           => ! [C: $i] :
                ( ( ssList @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ( ( B != D )
                      | ( A != C )
                      | ( ( ~ ( neq @ B @ nil )
                          | ~ ( singletonP @ C )
                          | ( singletonP @ A ) )
                        & ( ~ ( neq @ B @ nil )
                          | ( neq @ D @ nil ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(98,plain,
    ~ ! [A: $i] :
        ( ( ssList @ A )
       => ! [B: $i] :
            ( ( ssList @ B )
           => ! [C: $i] :
                ( ( ssList @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ( ( B != D )
                      | ( A != C )
                      | ( ( ~ ( neq @ B @ nil )
                          | ~ ( singletonP @ C )
                          | ( singletonP @ A ) )
                        & ( ~ ( neq @ B @ nil )
                          | ( neq @ D @ nil ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(108,plain,
    ( sk5
    | ( neq @ sk2 @ nil ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(100,plain,
    ( sk5
    | ~ ( neq @ sk4 @ nil ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(106,plain,
    sk2 = sk4,
    inference(cnf,[status(esa)],[98]) ).

thf(110,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[106]) ).

thf(504,plain,
    ( sk5
    | ~ ( neq @ sk2 @ nil ) ),
    inference(rewrite,[status(thm)],[100,110]) ).

thf(107,plain,
    ( ( singletonP @ sk3 )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(105,plain,
    sk1 = sk3,
    inference(cnf,[status(esa)],[98]) ).

thf(111,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[105]) ).

thf(509,plain,
    ( ( singletonP @ sk1 )
    | ~ sk5 ),
    inference(rewrite,[status(thm)],[107,111]) ).

thf(101,plain,
    ( ~ ( singletonP @ sk1 )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(510,plain,
    ( ~ sk5
    | ( ( singletonP @ sk1 )
     != ( singletonP @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[509,101]) ).

thf(511,plain,
    ~ sk5,
    inference(pattern_uni,[status(thm)],[510:[]]) ).

thf(514,plain,
    ( $false
    | ~ ( neq @ sk2 @ nil ) ),
    inference(rewrite,[status(thm)],[504,511]) ).

thf(515,plain,
    ~ ( neq @ sk2 @ nil ),
    inference(simp,[status(thm)],[514]) ).

thf(518,plain,
    ( $false
    | $false ),
    inference(rewrite,[status(thm)],[108,515,511]) ).

thf(519,plain,
    $false,
    inference(simp,[status(thm)],[518]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SWC255+1 : TPTP v8.2.0. Released v2.4.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Sun May 19 02:57:38 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.74/0.74  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.36/0.93  % [INFO] 	 Parsing done (186ms). 
% 1.36/0.94  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.59/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.89/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ... 
% 2.11/1.32  % [INFO] 	 Axiom selection finished. Selected 95 axioms (removed 0 axioms). 
% 2.31/1.43  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.31/1.44  % [INFO] 	 Type checking passed. 
% 2.31/1.44  % [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 ... 
% 5.73/2.46  % [INFO] 	 Killing All external provers ... 
% 5.73/2.46  % Time passed: 2025ms (effective reasoning time: 1516ms)
% 5.73/2.46  % 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)>
% 5.73/2.46  % Axioms used in derivation (0): 
% 5.73/2.46  % No. of inferences in proof: 19
% 5.73/2.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2025 ms resp. 1516 ms w/o parsing
% 5.73/2.48  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.73/2.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------