TSTP Solution File: SWC259-1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC259-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 04:34:40 EDT 2024

% Result   : Unsatisfiable 19.50s 5.41s
% Output   : Refutation 19.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   44 (  18 unt;   8 typ;   0 def)
%            Number of atoms       :   68 (  26 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  121 (  24   ~;  28   |;   0   &;  69   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   12 (   0   ^  12   !;   0   ?;  12   :)

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

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

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

thf(totalorderedP_type,type,
    totalorderedP: $i > $o ).

thf(ssItem_type,type,
    ssItem: $i > $o ).

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

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

thf(cons_type,type,
    cons: $i > $i > $i ).

thf(7,negated_conjecture,
    ~ ( totalorderedP @ sk1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

thf(219,plain,
    ~ ( totalorderedP @ sk1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(245,plain,
    ~ ( totalorderedP @ sk1 ),
    inference(polarity_switch,[status(thm)],[219]) ).

thf(9,negated_conjecture,
    ( ( ssItem @ sk5 )
    | ( nil = sk3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

thf(214,plain,
    ( ( ssItem @ sk5 )
    | ( nil = sk3 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(251,plain,
    ( ( ssItem @ sk5 )
    | ( nil = sk3 ) ),
    inference(cnf,[status(esa)],[214]) ).

thf(252,plain,
    ( ( nil = sk3 )
    | ( ssItem @ sk5 ) ),
    inference(lifteq,[status(thm)],[251]) ).

thf(6,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).

thf(212,plain,
    sk1 = sk3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(244,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[212]) ).

thf(942,plain,
    ( ( nil = sk1 )
    | ( ssItem @ sk5 ) ),
    inference(rewrite,[status(thm)],[252,244]) ).

thf(202,axiom,
    totalorderedP @ nil,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).

thf(672,plain,
    totalorderedP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(826,plain,
    ( ( totalorderedP @ nil )
   != ( totalorderedP @ sk1 ) ),
    inference(paramod_ordered,[status(thm)],[672,245]) ).

thf(829,plain,
    nil != sk1,
    inference(simp,[status(thm)],[826]) ).

thf(943,plain,
    ssItem @ sk5,
    inference(simplifyReflect,[status(thm)],[942,829]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( nil != A )
      | ~ ( ssList @ A )
      | ~ ( ssItem @ B )
      | ( totalorderedP @ ( cons @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause113) ).

thf(265,plain,
    ! [B: $i,A: $i] :
      ( ( nil != A )
      | ~ ( ssList @ A )
      | ~ ( ssItem @ B )
      | ( totalorderedP @ ( cons @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(266,plain,
    ! [B: $i,A: $i] :
      ( ( nil != A )
      | ~ ( ssList @ A )
      | ~ ( ssItem @ B )
      | ( totalorderedP @ ( cons @ B @ A ) ) ),
    inference(cnf,[status(esa)],[265]) ).

thf(267,plain,
    ! [B: $i,A: $i] :
      ( ( nil != A )
      | ~ ( ssList @ A )
      | ~ ( ssItem @ B )
      | ( totalorderedP @ ( cons @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[266]) ).

thf(268,plain,
    ! [A: $i] :
      ( ~ ( ssList @ nil )
      | ~ ( ssItem @ A )
      | ( totalorderedP @ ( cons @ A @ nil ) ) ),
    inference(simp,[status(thm)],[267]) ).

thf(50,axiom,
    ssList @ nil,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).

thf(325,plain,
    ssList @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(1258,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( ssItem @ A )
      | ( totalorderedP @ ( cons @ A @ nil ) ) ),
    inference(rewrite,[status(thm)],[268,325]) ).

thf(1259,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( totalorderedP @ ( cons @ A @ nil ) ) ),
    inference(simp,[status(thm)],[1258]) ).

thf(1269,plain,
    ! [A: $i] :
      ( ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk5 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[943,1259]) ).

thf(1270,plain,
    totalorderedP @ ( cons @ sk5 @ nil ),
    inference(pattern_uni,[status(thm)],[1269:[bind(A,$thf( sk5 ))]]) ).

thf(18,negated_conjecture,
    ( ( ( cons @ sk5 @ nil )
      = sk3 )
    | ( nil = sk3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).

thf(221,plain,
    ( ( ( cons @ sk5 @ nil )
      = sk3 )
    | ( nil = sk3 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(230,plain,
    ( ( ( cons @ sk5 @ nil )
      = sk3 )
    | ( nil = sk3 ) ),
    inference(cnf,[status(esa)],[221]) ).

thf(231,plain,
    ( ( ( cons @ sk5 @ nil )
      = sk3 )
    | ( nil = sk3 ) ),
    inference(lifteq,[status(thm)],[230]) ).

thf(684,plain,
    ( ( ( cons @ sk5 @ nil )
      = sk1 )
    | ( nil = sk1 ) ),
    inference(rewrite,[status(thm)],[231,244]) ).

thf(832,plain,
    ( ( cons @ sk5 @ nil )
    = sk1 ),
    inference(simplifyReflect,[status(thm)],[684,829]) ).

thf(1302,plain,
    totalorderedP @ sk1,
    inference(rewrite,[status(thm)],[1270,832]) ).

thf(1303,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[245,1302]) ).

thf(1304,plain,
    $false,
    inference(simp,[status(thm)],[1303]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWC259-1 : TPTP v8.2.0. Released v2.4.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun May 19 02:54:09 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.16/1.14  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.09/1.45  % [INFO] 	 Parsing done (304ms). 
% 2.09/1.46  % [INFO] 	 Running in sequential loop mode. 
% 3.02/1.92  % [INFO] 	 nitpick registered as external prover. 
% 3.02/1.93  % [INFO] 	 Scanning for conjecture ... 
% 3.59/2.10  % [INFO] 	 Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ... 
% 4.14/2.26  % [INFO] 	 Axiom selection finished. Selected 185 axioms (removed 0 axioms). 
% 4.69/2.42  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.73/2.44  % [INFO] 	 Type checking passed. 
% 4.73/2.45  % [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 ... 
% 19.50/5.39  % [INFO] 	 Killing All external provers ... 
% 19.50/5.40  % Time passed: 4868ms (effective reasoning time: 3930ms)
% 19.50/5.41  % Axioms used in derivation (3): clause4, clause113, clause8
% 19.50/5.41  % No. of inferences in proof: 36
% 19.50/5.41  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4868 ms resp. 3930 ms w/o parsing
% 19.50/5.44  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.50/5.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------