TSTP Solution File: SWC322-1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC322-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 04:34:54 EDT 2024

% Result   : Unsatisfiable 14.46s 3.55s
% Output   : Refutation 14.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   81 (  14 unt;  11 typ;   0 def)
%            Number of atoms       :  149 ( 102 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  368 (  79   ~;  79   |;   0   &; 210   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   14 (   0   ^  14   !;   0   ?;  14   :)

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

thf(app_type,type,
    app: $i > $i > $i ).

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

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

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

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

thf(12,negated_conjecture,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( nil = sk2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).

thf(210,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( nil = sk2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(227,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( nil = sk2 ) ),
    inference(cnf,[status(esa)],[210]) ).

thf(228,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( nil = sk2 ) ),
    inference(lifteq,[status(thm)],[227]) ).

thf(8,negated_conjecture,
    ( ( nil = sk3 )
    | ( nil != sk4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

thf(215,plain,
    ( ( nil = sk3 )
    | ( nil != sk4 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(229,plain,
    ( ( nil = sk3 )
    | ( nil != sk4 ) ),
    inference(cnf,[status(esa)],[215]) ).

thf(230,plain,
    ( ( nil = sk3 )
    | ( nil != sk4 ) ),
    inference(lifteq,[status(thm)],[229]) ).

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

thf(202,plain,
    sk2 = sk4,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(233,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[202]) ).

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

thf(206,plain,
    sk1 = sk3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(218,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[206]) ).

thf(666,plain,
    ( ( nil = sk1 )
    | ( nil != sk2 ) ),
    inference(rewrite,[status(thm)],[230,233,218]) ).

thf(15,negated_conjecture,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( nil != sk1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).

thf(217,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( nil != sk1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(231,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( nil != sk1 ) ),
    inference(cnf,[status(esa)],[217]) ).

thf(232,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
      = sk2 )
    | ( nil != sk1 ) ),
    inference(lifteq,[status(thm)],[231]) ).

thf(7,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ( ( app @ ( cons @ A @ nil ) @ B )
        = sk3 )
      | ( ( app @ B @ ( cons @ A @ nil ) )
       != sk4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

thf(211,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ( ( app @ ( cons @ A @ nil ) @ B )
        = sk3 )
      | ( ( app @ B @ ( cons @ A @ nil ) )
       != sk4 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(234,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ( ( app @ ( cons @ A @ nil ) @ B )
        = sk3 )
      | ( ( app @ B @ ( cons @ A @ nil ) )
       != sk4 ) ),
    inference(cnf,[status(esa)],[211]) ).

thf(235,plain,
    ! [B: $i,A: $i] :
      ( ( ( app @ ( cons @ A @ nil ) @ B )
        = sk3 )
      | ( ( app @ B @ ( cons @ A @ nil ) )
       != sk4 )
      | ~ ( ssItem @ A )
      | ~ ( ssList @ B ) ),
    inference(lifteq,[status(thm)],[234]) ).

thf(863,plain,
    ! [B: $i,A: $i] :
      ( ( ( app @ ( cons @ A @ nil ) @ B )
        = sk1 )
      | ( ( app @ B @ ( cons @ A @ nil ) )
       != sk2 )
      | ~ ( ssItem @ A )
      | ~ ( ssList @ B ) ),
    inference(rewrite,[status(thm)],[235,233,218]) ).

thf(16,negated_conjecture,
    ( ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
     != sk1 )
    | ( nil != sk1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).

thf(213,plain,
    ( ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
     != sk1 )
    | ( nil != sk1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(223,plain,
    ( ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
     != sk1 )
    | ( nil != sk1 ) ),
    inference(cnf,[status(esa)],[213]) ).

thf(224,plain,
    ( ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
     != sk1 )
    | ( nil != sk1 ) ),
    inference(lifteq,[status(thm)],[223]) ).

thf(870,plain,
    ! [B: $i,A: $i] :
      ( ( ( app @ B @ ( cons @ A @ nil ) )
       != sk2 )
      | ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ( nil != sk1 )
      | ( ( app @ ( cons @ A @ nil ) @ B )
       != ( app @ ( cons @ sk5 @ nil ) @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[863,224]) ).

thf(871,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
     != sk2 )
    | ~ ( ssItem @ sk5 )
    | ~ ( ssList @ sk6 )
    | ( nil != sk1 ) ),
    inference(pattern_uni,[status(thm)],[870:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(9,negated_conjecture,
    ( ( ssItem @ sk5 )
    | ( nil = sk2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

thf(207,plain,
    ( ( ssItem @ sk5 )
    | ( nil = sk2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(236,plain,
    ( ( ssItem @ sk5 )
    | ( nil = sk2 ) ),
    inference(cnf,[status(esa)],[207]) ).

thf(237,plain,
    ( ( nil = sk2 )
    | ( ssItem @ sk5 ) ),
    inference(lifteq,[status(thm)],[236]) ).

thf(677,plain,
    ( ( ssItem @ sk5 )
    | ( nil = sk1 )
    | ( nil != nil ) ),
    inference(paramod_ordered,[status(thm)],[237,666]) ).

thf(678,plain,
    ( ( ssItem @ sk5 )
    | ( nil = sk1 ) ),
    inference(pattern_uni,[status(thm)],[677:[]]) ).

thf(10,negated_conjecture,
    ( ( ssItem @ sk5 )
    | ( nil != sk1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

thf(203,plain,
    ( ( ssItem @ sk5 )
    | ( nil != sk1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(225,plain,
    ( ( ssItem @ sk5 )
    | ( nil != sk1 ) ),
    inference(cnf,[status(esa)],[203]) ).

thf(226,plain,
    ( ( nil != sk1 )
    | ( ssItem @ sk5 ) ),
    inference(lifteq,[status(thm)],[225]) ).

thf(833,plain,
    ( ( ssItem @ sk5 )
    | ( nil != nil ) ),
    inference(paramod_ordered,[status(thm)],[678,226]) ).

thf(834,plain,
    ssItem @ sk5,
    inference(pattern_uni,[status(thm)],[833:[]]) ).

thf(11,negated_conjecture,
    ( ( ssList @ sk6 )
    | ( nil = sk2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).

thf(214,plain,
    ( ( ssList @ sk6 )
    | ( nil = sk2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(238,plain,
    ( ( ssList @ sk6 )
    | ( nil = sk2 ) ),
    inference(cnf,[status(esa)],[214]) ).

thf(239,plain,
    ( ( nil = sk2 )
    | ( ssList @ sk6 ) ),
    inference(lifteq,[status(thm)],[238]) ).

thf(717,plain,
    ( ( ssList @ sk6 )
    | ( nil = sk1 )
    | ( nil != nil ) ),
    inference(paramod_ordered,[status(thm)],[239,666]) ).

thf(718,plain,
    ( ( ssList @ sk6 )
    | ( nil = sk1 ) ),
    inference(pattern_uni,[status(thm)],[717:[]]) ).

thf(14,negated_conjecture,
    ( ( ssList @ sk6 )
    | ( nil != sk1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).

thf(204,plain,
    ( ( ssList @ sk6 )
    | ( nil != sk1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(219,plain,
    ( ( ssList @ sk6 )
    | ( nil != sk1 ) ),
    inference(cnf,[status(esa)],[204]) ).

thf(220,plain,
    ( ( nil != sk1 )
    | ( ssList @ sk6 ) ),
    inference(lifteq,[status(thm)],[219]) ).

thf(1126,plain,
    ( ( ssList @ sk6 )
    | ( nil != nil ) ),
    inference(paramod_ordered,[status(thm)],[718,220]) ).

thf(1127,plain,
    ssList @ sk6,
    inference(pattern_uni,[status(thm)],[1126:[]]) ).

thf(1269,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
     != sk2 )
    | ~ $true
    | ~ $true
    | ( nil != sk1 ) ),
    inference(rewrite,[status(thm)],[871,834,1127]) ).

thf(1270,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
     != sk2 )
    | ( nil != sk1 ) ),
    inference(simp,[status(thm)],[1269]) ).

thf(1274,plain,
    ( ( nil != sk1 )
    | ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
     != ( app @ sk6 @ ( cons @ sk5 @ nil ) ) ) ),
    inference(paramod_ordered,[status(thm)],[232,1270]) ).

thf(1275,plain,
    nil != sk1,
    inference(pattern_uni,[status(thm)],[1274:[]]) ).

thf(1278,plain,
    nil != sk2,
    inference(simplifyReflect,[status(thm)],[666,1275]) ).

thf(1280,plain,
    ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
    = sk2 ),
    inference(simplifyReflect,[status(thm)],[228,1278]) ).

thf(13,negated_conjecture,
    ( ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
     != sk1 )
    | ( nil = sk2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).

thf(208,plain,
    ( ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
     != sk1 )
    | ( nil = sk2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(221,plain,
    ( ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
     != sk1 )
    | ( nil = sk2 ) ),
    inference(cnf,[status(esa)],[208]) ).

thf(222,plain,
    ( ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
     != sk1 )
    | ( nil = sk2 ) ),
    inference(lifteq,[status(thm)],[221]) ).

thf(1281,plain,
    ( ( app @ ( cons @ sk5 @ nil ) @ sk6 )
   != sk1 ),
    inference(simplifyReflect,[status(thm)],[222,1278]) ).

thf(1333,plain,
    ! [B: $i,A: $i] :
      ( ( ( app @ B @ ( cons @ A @ nil ) )
       != sk2 )
      | ~ ( ssItem @ A )
      | ~ ( ssList @ B )
      | ( ( app @ ( cons @ A @ nil ) @ B )
       != ( app @ ( cons @ sk5 @ nil ) @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[863,1281]) ).

thf(1334,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
     != sk2 )
    | ~ ( ssItem @ sk5 )
    | ~ ( ssList @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[1333:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(1335,plain,
    ( ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
     != sk2 )
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[1334,834,1127]) ).

thf(1336,plain,
    ( ( app @ sk6 @ ( cons @ sk5 @ nil ) )
   != sk2 ),
    inference(simp,[status(thm)],[1335]) ).

thf(2081,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[1280,1336]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC322-1 : TPTP v8.2.0. Released v2.4.0.
% 0.16/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n020.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 03:55:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.92/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.35/1.00  % [INFO] 	 Parsing done (152ms). 
% 1.35/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.87/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.87/1.21  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ... 
% 2.47/1.37  % [INFO] 	 Axiom selection finished. Selected 185 axioms (removed 0 axioms). 
% 2.77/1.46  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.77/1.46  % [INFO] 	 Type checking passed. 
% 2.77/1.47  % [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 ... 
% 14.46/3.54  % [INFO] 	 Killing All external provers ... 
% 14.46/3.55  % Time passed: 3021ms (effective reasoning time: 2528ms)
% 14.46/3.55  % Axioms used in derivation (0): 
% 14.46/3.55  % No. of inferences in proof: 70
% 14.46/3.55  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3021 ms resp. 2528 ms w/o parsing
% 14.46/3.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.46/3.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------