TSTP Solution File: SWC094-1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC094-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 04:34:01 EDT 2024

% Result   : Unsatisfiable 197.25s 29.75s
% Output   : Refutation 197.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   49 (  20 unt;   7 typ;   0 def)
%            Number of atoms       :   99 (  56 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  271 (  69   ~;  49   |;   0   &; 153   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   7 con; 0-2 aty)
%            Number of variables   :   31 (   0   ^  31   !;   0   ?;  31   :)

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

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

thf(101,axiom,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ nil @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).

thf(395,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ nil @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(396,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( app @ nil @ A )
        = A ) ),
    inference(cnf,[status(esa)],[395]) ).

thf(397,plain,
    ! [A: $i] :
      ( ( ( app @ nil @ A )
        = A )
      | ~ ( ssList @ A ) ),
    inference(lifteq,[status(thm)],[396]) ).

thf(83,axiom,
    ssList @ nil,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).

thf(349,plain,
    ssList @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(1,negated_conjecture,
    ssList @ sk1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).

thf(195,plain,
    ssList @ sk1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(8,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ( ( app @ ( app @ A @ B ) @ C )
       != sk1 )
      | ( ( app @ A @ C )
       != sk2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

thf(200,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ( ( app @ ( app @ A @ B ) @ C )
       != sk1 )
      | ( ( app @ A @ C )
       != sk2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C )
      | ( ( app @ ( app @ A @ B ) @ C )
       != sk1 )
      | ( ( app @ A @ C )
       != sk2 ) ),
    inference(cnf,[status(esa)],[200]) ).

thf(206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ A @ B ) @ C )
       != sk1 )
      | ( ( app @ A @ C )
       != sk2 )
      | ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C ) ),
    inference(lifteq,[status(thm)],[205]) ).

thf(5,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).

thf(194,plain,
    sk2 = sk4,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(204,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[194]) ).

thf(7,negated_conjecture,
    sk4 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

thf(198,plain,
    sk4 = sk3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(203,plain,
    sk4 = sk3,
    inference(lifteq,[status(thm)],[198]) ).

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

thf(196,plain,
    sk1 = sk3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(202,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[196]) ).

thf(630,plain,
    sk4 = sk1,
    inference(rewrite,[status(thm)],[203,202]) ).

thf(632,plain,
    sk2 = sk1,
    inference(rewrite,[status(thm)],[204,630]) ).

thf(634,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ A @ B ) @ C )
       != sk1 )
      | ( ( app @ A @ C )
       != sk1 )
      | ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ~ ( ssList @ C ) ),
    inference(rewrite,[status(thm)],[206,632]) ).

thf(639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( app @ ( app @ A @ B ) @ C )
       != sk1 )
      | ( ( app @ A @ C )
       != sk1 )
      | ~ ( ssList @ A )
      | ~ ( ssList @ B )
      | ( ( ssList @ sk1 )
       != ( ssList @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[195,634]) ).

thf(640,plain,
    ! [B: $i,A: $i] :
      ( ( ( app @ ( app @ A @ B ) @ sk1 )
       != sk1 )
      | ( ( app @ A @ sk1 )
       != sk1 )
      | ~ ( ssList @ A )
      | ~ ( ssList @ B ) ),
    inference(pattern_uni,[status(thm)],[639:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).

thf(686,plain,
    ! [B: $i,A: $i] :
      ( ( ( app @ ( app @ A @ B ) @ sk1 )
       != sk1 )
      | ( ( app @ A @ sk1 )
       != sk1 )
      | ~ ( ssList @ B )
      | ( ( ssList @ nil )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[349,640]) ).

thf(687,plain,
    ! [A: $i] :
      ( ( ( app @ ( app @ nil @ A ) @ sk1 )
       != sk1 )
      | ( ( app @ nil @ sk1 )
       != sk1 )
      | ~ ( ssList @ A ) ),
    inference(pattern_uni,[status(thm)],[686:[bind(A,$thf( nil ))]]) ).

thf(694,plain,
    ! [A: $i] :
      ( ( ( app @ ( app @ nil @ A ) @ sk1 )
       != sk1 )
      | ( ( app @ nil @ sk1 )
       != sk1 )
      | ~ ( ssList @ A ) ),
    inference(simp,[status(thm)],[687]) ).

thf(913,plain,
    ! [A: $i] :
      ( ( ( app @ ( app @ nil @ A ) @ sk1 )
       != sk1 )
      | ( ( app @ nil @ sk1 )
       != sk1 )
      | ( ( ssList @ nil )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[349,694]) ).

thf(914,plain,
    ( ( ( app @ ( app @ nil @ nil ) @ sk1 )
     != sk1 )
    | ( ( app @ nil @ sk1 )
     != sk1 ) ),
    inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( nil ))]]) ).

thf(1195,plain,
    ( ( ( app @ nil @ sk1 )
     != sk1 )
    | ( ( app @ ( app @ nil @ nil ) @ sk1 )
     != ( app @ nil @ sk1 ) )
    | ( sk1 != sk1 ) ),
    inference(eqfactor_ordered,[status(thm)],[914]) ).

thf(1196,plain,
    ( ( ( app @ nil @ sk1 )
     != sk1 )
    | ( ( app @ ( app @ nil @ nil ) @ sk1 )
     != ( app @ nil @ sk1 ) ) ),
    inference(simp,[status(thm)],[1195]) ).

thf(66629,plain,
    ! [A: $i] :
      ( ( ( app @ nil @ A )
        = A )
      | ( ( ssList @ nil )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[349,397]) ).

thf(66630,plain,
    ( ( app @ nil @ nil )
    = nil ),
    inference(pattern_uni,[status(thm)],[66629:[bind(A,$thf( nil ))]]) ).

thf(67257,plain,
    ( ( ( app @ nil @ sk1 )
     != sk1 )
    | ( ( app @ nil @ sk1 )
     != ( app @ nil @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[1196,66630]) ).

thf(67258,plain,
    ( ( app @ nil @ sk1 )
   != sk1 ),
    inference(simp,[status(thm)],[67257]) ).

thf(68186,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( A != sk1 )
      | ( ( app @ nil @ A )
       != ( app @ nil @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[397,67258]) ).

thf(68187,plain,
    ( ~ ( ssList @ sk1 )
    | ( sk1 != sk1 ) ),
    inference(pattern_uni,[status(thm)],[68186:[bind(A,$thf( sk1 ))]]) ).

thf(68299,plain,
    ~ ( ssList @ sk1 ),
    inference(simp,[status(thm)],[68187]) ).

thf(68305,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[68299,195]) ).

thf(68306,plain,
    $false,
    inference(simp,[status(thm)],[68305]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC094-1 : TPTP v8.2.0. Released v2.4.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n018.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 03:44:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.58/1.09  % [INFO] 	 Parsing done (175ms). 
% 1.58/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.90/1.29  % [INFO] 	 nitpick registered as external prover. 
% 1.90/1.30  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ... 
% 2.52/1.46  % [INFO] 	 Axiom selection finished. Selected 185 axioms (removed 0 axioms). 
% 2.89/1.56  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.89/1.57  % [INFO] 	 Type checking passed. 
% 2.89/1.57  % [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 ... 
% 197.25/29.74  % [INFO] 	 Killing All external provers ... 
% 197.25/29.75  % Time passed: 29205ms (effective reasoning time: 28639ms)
% 197.25/29.75  % Axioms used in derivation (2): clause74, clause8
% 197.25/29.75  % No. of inferences in proof: 42
% 197.25/29.75  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 29205 ms resp. 28639 ms w/o parsing
% 197.28/29.79  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 197.28/29.79  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------