TSTP Solution File: SWW410-1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW410-1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 : Fri May 19 12:23:51 EDT 2023

% Result   : Unsatisfiable 3.13s 1.64s
% Output   : Refutation 3.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   44 (  21 unt;   9 typ;   0 def)
%            Number of atoms       :   55 (  24 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  334 (  28   ~;  20   |;   0   &; 286   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   76 (   0   ^;  76   !;   0   ?;  76   :)

% Comments : 
%------------------------------------------------------------------------------
thf(heap_type,type,
    heap: $i > $o ).

thf(sep_type,type,
    sep: $i > $i > $i ).

thf(lseg_type,type,
    lseg: $i > $i > $i ).

thf(x3_type,type,
    x3: $i ).

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

thf(x2_type,type,
    x2: $i ).

thf(emp_type,type,
    emp: $i ).

thf(x1_type,type,
    x1: $i ).

thf(next_type,type,
    next: $i > $i > $i ).

thf(4,axiom,
    x1 != x3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_3) ).

thf(25,plain,
    x1 != x3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normalization) ).

thf(52,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( next @ A @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_3) ).

thf(41,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( next @ A @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(3,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) )
      | ( C = D )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unfolding_5) ).

thf(22,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) )
      | ( C = D )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ ( sep @ ( next @ C @ D ) @ E ) ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ ( sep @ ( next @ C @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unfolding_4) ).

thf(39,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ ( sep @ ( next @ C @ D ) @ E ) ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ ( sep @ ( next @ C @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(1,negated_conjecture,
    ~ ( heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x2 @ x3 ) @ emp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_1) ).

thf(18,plain,
    ~ ( heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ x2 @ x3 ) @ emp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unfolding_3) ).

thf(31,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(12,axiom,
    nil != x2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_2) ).

thf(43,plain,
    nil != x2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_4) ).

thf(36,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_commutative) ).

thf(20,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
      | ( A = B )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unfolding_2) ).

thf(46,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
      | ( A = B )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
      | ( A = nil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_2) ).

thf(57,plain,
    ! [B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
      | ( A = nil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_1) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( next @ x1 @ x3 ) @ emp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_5) ).

thf(28,plain,
    heap @ ( sep @ ( lseg @ x2 @ x1 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( next @ x1 @ x3 ) @ emp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    x3 != x2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_4) ).

thf(33,plain,
    x3 != x2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(16,axiom,
    nil != x1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_1) ).

thf(54,plain,
    nil != x1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
      | ( A = B )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellformedness_5) ).

thf(49,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
      | ( A = B )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(60,plain,
    $false,
    inference(e,[status(thm)],[25,52,41,22,39,18,31,43,36,20,46,57,29,28,33,54,49]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW410-1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n019.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu May 18 22:31:43 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.85/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.11/0.92  % [INFO] 	 Parsing done (117ms). 
% 1.11/0.93  % [INFO] 	 Running in sequential loop mode. 
% 1.52/1.13  % [INFO] 	 eprover registered as external prover. 
% 1.52/1.13  % [INFO] 	 cvc4 registered as external prover. 
% 1.52/1.14  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.20  % [INFO] 	 Found a conjecture and 16 axioms. Running axiom selection ... 
% 1.94/1.24  % [INFO] 	 Axiom selection finished. Selected 16 axioms (removed 0 axioms). 
% 1.94/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.94/1.26  % [INFO] 	 Type checking passed. 
% 1.94/1.26  % [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 ... 
% 3.13/1.63  % External prover 'e' found a proof!
% 3.13/1.63  % [INFO] 	 Killing All external provers ... 
% 3.13/1.63  % Time passed: 1107ms (effective reasoning time: 704ms)
% 3.13/1.63  % 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)>
% 3.13/1.64  % Axioms used in derivation (16): premise_5, premise_2, wellformedness_2, wellformedness_3, wellformedness_4, premise_3, unfolding_2, premise_1, premise_4, wellformedness_1, wellformedness_5, associative_commutative, unfolding_5, normalization, unfolding_3, unfolding_4
% 3.13/1.64  % No. of inferences in proof: 35
% 3.13/1.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1107 ms resp. 704 ms w/o parsing
% 3.42/1.71  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.42/1.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------