TSTP Solution File: SEU494^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU494^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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  : 300s
% DateTime : Tue May 21 03:42:17 EDT 2024

% Result   : Theorem 9.99s 2.99s
% Output   : Refutation 9.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   44 (   9 unt;   8 typ;   2 def)
%            Number of atoms       :   94 (  10 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  244 (  31   ~;  35   |;   5   &; 166   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   9 con; 0-3 aty)
%            Number of variables   :   39 (   4   ^  35   !;   0   ?;  39   :)

% Comments : 
%------------------------------------------------------------------------------
thf(inv_type,type,
    inv: ( $i > $i > $o ) > $i > $i > $o ).

thf(inv_def,definition,
    ( inv
    = ( ^ [A: $i > $i > $o,B: $i,C: $i] : ( A @ C @ B ) ) ) ).

thf(so_type,type,
    so: ( $i > $i > $o ) > $o ).

thf(so_def,definition,
    ( so
    = ( ^ [A: $i > $i > $o] :
          ( ( asymm @ A )
          & ( trans @ A ) ) ) ) ).

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

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

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

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

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

thf(sk6_type,type,
    sk6: $i ).

thf(1,conjecture,
    ! [A: $i > $i > $o] :
      ( ( so @ A )
     => ( so @ ( inv @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_of_strict_order_is_strict_order) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o] :
        ( ( so @ A )
       => ( so @ ( inv @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i > $i > $o] :
        ( ( ! [B: $i,C: $i] :
              ( ( A @ B @ C )
             => ~ ( A @ C @ B ) )
          & ! [B: $i,C: $i,D: $i] :
              ( ( ( A @ B @ C )
                & ( A @ C @ D ) )
             => ( A @ B @ D ) ) )
       => ( ! [B: $i,C: $i] :
              ( ( A @ C @ B )
             => ~ ( A @ B @ C ) )
          & ! [B: $i,C: $i,D: $i] :
              ( ( ( A @ C @ B )
                & ( A @ D @ C ) )
             => ( A @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ( ( sk1 @ sk2 @ sk3 )
    | ( sk1 @ sk6 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(55,plain,
    ( ( sk1 @ sk2 @ sk3 )
    | ( ( sk1 @ sk6 @ sk5 )
     != ( sk1 @ sk2 @ sk3 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[9]) ).

thf(57,plain,
    ( ( sk1 @ sk2 @ sk3 )
    | ( ( sk1 @ sk6 @ sk5 )
     != ( sk1 @ sk2 @ sk3 ) ) ),
    inference(simp,[status(thm)],[55]) ).

thf(7,plain,
    ( ( sk1 @ sk3 @ sk2 )
    | ( sk1 @ sk6 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ( ( sk1 @ sk3 @ sk2 )
    | ( sk1 @ sk5 @ sk4 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ~ ( sk1 @ B @ C )
      | ( sk1 @ A @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ~ ( sk1 @ B @ C )
      | ( sk1 @ A @ C ) ),
    inference(simp,[status(thm)],[6]) ).

thf(162,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk1 @ sk3 @ sk2 )
      | ~ ( sk1 @ A @ B )
      | ( sk1 @ A @ C )
      | ( ( sk1 @ sk5 @ sk4 )
       != ( sk1 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[10,12]) ).

thf(163,plain,
    ! [A: $i] :
      ( ( sk1 @ sk3 @ sk2 )
      | ~ ( sk1 @ A @ sk5 )
      | ( sk1 @ A @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( A )),bind(B,$thf( sk5 )),bind(C,$thf( sk4 ))]]) ).

thf(621,plain,
    ! [A: $i] :
      ( ( sk1 @ sk3 @ sk2 )
      | ( sk1 @ A @ sk4 )
      | ( ( sk1 @ sk6 @ sk5 )
       != ( sk1 @ A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[7,163]) ).

thf(622,plain,
    ( ( sk1 @ sk3 @ sk2 )
    | ( sk1 @ sk6 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[621:[bind(A,$thf( sk6 ))]]) ).

thf(8,plain,
    ( ( sk1 @ sk3 @ sk2 )
    | ~ ( sk1 @ sk6 @ sk4 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(687,plain,
    ( ( sk1 @ sk3 @ sk2 )
    | ( ( sk1 @ sk6 @ sk4 )
     != ( sk1 @ sk6 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[622,8]) ).

thf(688,plain,
    sk1 @ sk3 @ sk2,
    inference(pattern_uni,[status(thm)],[687:[]]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ~ ( sk1 @ B @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(724,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ B @ A )
      | ( ( sk1 @ sk3 @ sk2 )
       != ( sk1 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[688,11]) ).

thf(725,plain,
    ~ ( sk1 @ sk2 @ sk3 ),
    inference(pattern_uni,[status(thm)],[724:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).

thf(743,plain,
    ( $false
    | ( sk1 @ sk6 @ sk5 ) ),
    inference(rewrite,[status(thm)],[57,725]) ).

thf(744,plain,
    sk1 @ sk6 @ sk5,
    inference(simp,[status(thm)],[743]) ).

thf(4,plain,
    ( ( sk1 @ sk2 @ sk3 )
    | ( sk1 @ sk5 @ sk4 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(184,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sk1 @ sk2 @ sk3 )
      | ~ ( sk1 @ A @ B )
      | ( sk1 @ A @ C )
      | ( ( sk1 @ sk5 @ sk4 )
       != ( sk1 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[4,12]) ).

thf(185,plain,
    ! [A: $i] :
      ( ( sk1 @ sk2 @ sk3 )
      | ~ ( sk1 @ A @ sk5 )
      | ( sk1 @ A @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( A )),bind(B,$thf( sk5 )),bind(C,$thf( sk4 ))]]) ).

thf(1364,plain,
    ! [A: $i] :
      ( $false
      | ~ ( sk1 @ A @ sk5 )
      | ( sk1 @ A @ sk4 ) ),
    inference(rewrite,[status(thm)],[185,725]) ).

thf(1365,plain,
    ! [A: $i] :
      ( ~ ( sk1 @ A @ sk5 )
      | ( sk1 @ A @ sk4 ) ),
    inference(simp,[status(thm)],[1364]) ).

thf(1374,plain,
    ! [A: $i] :
      ( ( sk1 @ A @ sk4 )
      | ( ( sk1 @ sk6 @ sk5 )
       != ( sk1 @ A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[744,1365]) ).

thf(1375,plain,
    sk1 @ sk6 @ sk4,
    inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( sk6 ))]]) ).

thf(5,plain,
    ( ( sk1 @ sk2 @ sk3 )
    | ~ ( sk1 @ sk6 @ sk4 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(741,plain,
    ( $false
    | ~ ( sk1 @ sk6 @ sk4 ) ),
    inference(rewrite,[status(thm)],[5,725]) ).

thf(742,plain,
    ~ ( sk1 @ sk6 @ sk4 ),
    inference(simp,[status(thm)],[741]) ).

thf(1391,plain,
    $false,
    inference(rewrite,[status(thm)],[1375,742]) ).

thf(1392,plain,
    $false,
    inference(simp,[status(thm)],[1391]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU494^1 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n009.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 17:11:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.06/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.45/1.10  % [INFO] 	 Parsing done (162ms). 
% 1.45/1.11  % [INFO] 	 Running in sequential loop mode. 
% 2.03/1.33  % [INFO] 	 nitpick registered as external prover. 
% 2.03/1.33  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.23/1.45  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.23/1.45  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.45/1.46  % [INFO] 	 Type checking passed. 
% 2.45/1.46  % [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 ... 
% 9.99/2.97  % [INFO] 	 Killing All external provers ... 
% 9.99/2.97  % Time passed: 2429ms (effective reasoning time: 1854ms)
% 9.99/2.97  % 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)>
% 9.99/2.98  % Axioms used in derivation (0): 
% 9.99/2.98  % No. of inferences in proof: 34
% 9.99/2.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2429 ms resp. 1854 ms w/o parsing
% 9.99/3.04  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.99/3.04  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------