TSTP Solution File: SWW413-1 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW413-1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% 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 : Mon Jun 24 18:25:06 EDT 2024

% Result   : Unsatisfiable 89.55s 15.87s
% Output   : Refutation 89.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   38 (  23 unt;   0 typ;   0 def)
%            Number of atoms       :   62 (  32 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  400 (  22   ~;  22   |;   0   &; 356   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   74 (   0   ^  74   !;   0   ?;  74   :)

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

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

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

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

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

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).

thf(51,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(52,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(lifteq,[status(thm)],[51]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_commutative) ).

thf(25,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)],[3]) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[25]) ).

thf(81,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sep @ D @ ( sep @ B @ ( sep @ A @ C ) ) )
        = ( sep @ E @ ( sep @ D @ F ) ) )
      | ( ( sep @ A @ ( sep @ B @ C ) )
       != ( sep @ E @ F ) ) ),
    inference(paramod_ordered,[status(thm)],[26,26]) ).

thf(82,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) )
      = ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) ) ),
    inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( sep @ G @ H ))]]) ).

thf(102,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) )
      = ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) ) ),
    inference(simp,[status(thm)],[82]) ).

thf(17,axiom,
    heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( next @ x2 @ x3 ) @ emp ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_7) ).

thf(62,plain,
    heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( next @ x2 @ x3 ) @ emp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(77,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ B @ ( sep @ A @ C ) ) ) )
      | ( ( sep @ A @ ( sep @ B @ C ) )
       != ( sep @ ( next @ x2 @ x3 ) @ emp ) ) ),
    inference(paramod_ordered,[status(thm)],[26,62]) ).

thf(89,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ B @ ( sep @ A @ C ) ) ) )
      | ( A
       != ( next @ x2 @ x3 ) )
      | ( ( sep @ B @ C )
       != emp ) ),
    inference(simp,[status(thm)],[77]) ).

thf(106,plain,
    ! [B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ A @ ( sep @ ( next @ x2 @ x3 ) @ B ) ) ) )
      | ( ( sep @ A @ B )
       != emp ) ),
    inference(simp,[status(thm)],[89]) ).

thf(25906,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ C @ ( sep @ ( next @ x2 @ x3 ) @ D ) ) ) )
      | ( B != emp )
      | ( ( sep @ ( lseg @ A @ A ) @ B )
       != ( sep @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[52,106]) ).

thf(25907,plain,
    ! [B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ B @ B ) @ ( sep @ ( next @ x2 @ x3 ) @ A ) ) ) )
      | ( A != emp ) ),
    inference(pattern_uni,[status(thm)],[25906:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( lseg @ F @ F )),bind(D,$thf( B ))]]) ).

thf(26421,plain,
    ! [A: $i] : ( heap @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( next @ x2 @ x3 ) @ emp ) ) ) ),
    inference(simp,[status(thm)],[25907]) ).

thf(26927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) ) )
      | ( ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) )
       != ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ E @ E ) @ ( sep @ ( next @ x2 @ x3 ) @ emp ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[102,26421]) ).

thf(26928,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x2 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ A @ A ) @ emp ) ) ) ),
    inference(pattern_uni,[status(thm)],[26927:[bind(A,$thf( next @ x2 @ x3 )),bind(B,$thf( lseg @ x3 @ nil )),bind(C,$thf( lseg @ I @ I )),bind(D,$thf( emp )),bind(E,$thf( I ))]]) ).

thf(27348,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x2 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ ( sep @ ( lseg @ A @ A ) @ emp ) ) ) ),
    inference(simp,[status(thm)],[26928]) ).

thf(36176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x2 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ B ) ) )
      | ( ( sep @ ( lseg @ A @ A ) @ B )
       != ( sep @ ( lseg @ C @ C ) @ emp ) ) ),
    inference(paramod_ordered,[status(thm)],[52,27348]) ).

thf(36177,plain,
    heap @ ( sep @ ( next @ x2 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ),
    inference(pattern_uni,[status(thm)],[36176:[bind(A,$thf( A )),bind(B,$thf( emp )),bind(C,$thf( A ))]]) ).

thf(10,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/sandbox/benchmark/theBenchmark.p',unfolding_2) ).

thf(43,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)],[10]) ).

thf(44,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(cnf,[status(esa)],[43]) ).

thf(45,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) ) ),
    inference(lifteq,[status(thm)],[44]) ).

thf(36903,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) )
      | ( ( heap @ ( sep @ ( next @ x2 @ x3 ) @ ( sep @ ( lseg @ x3 @ nil ) @ emp ) ) )
       != ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[36177,45]) ).

thf(36904,plain,
    ( ( x3 = x2 )
    | ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ emp ) ) ),
    inference(pattern_uni,[status(thm)],[36903:[bind(A,$thf( x2 )),bind(B,$thf( x3 )),bind(C,$thf( nil )),bind(D,$thf( emp ))]]) ).

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

thf(20,plain,
    ~ ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ emp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(21,plain,
    ~ ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ emp ) ),
    inference(polarity_switch,[status(thm)],[20]) ).

thf(38091,plain,
    ( ( x3 = x2 )
    | $false ),
    inference(rewrite,[status(thm)],[36904,21]) ).

thf(38092,plain,
    x3 = x2,
    inference(simp,[status(thm)],[38091]) ).

thf(19,axiom,
    x3 != x2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).

thf(65,plain,
    x3 != x2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(66,plain,
    x3 != x2,
    inference(polarity_switch,[status(thm)],[65]) ).

thf(67,plain,
    x3 != x2,
    inference(lifteq,[status(thm)],[66]) ).

thf(38093,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[38092,67]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SWW413-1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.09  % Command  : run_Leo-III %s %d SAT
% 0.08/0.29  % Computer : n018.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit : 300
% 0.08/0.29  % WCLimit  : 300
% 0.08/0.29  % DateTime : Wed Jun 19 08:40:25 EDT 2024
% 0.08/0.29  % CPUTime  : 
% 0.62/0.70  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.93/0.82  % [INFO] 	 Parsing done (113ms). 
% 0.93/0.83  % [INFO] 	 Running in sequential loop mode. 
% 1.34/1.05  % [INFO] 	 nitpick registered as external prover. 
% 1.34/1.05  % [INFO] 	 Scanning for conjecture ... 
% 1.54/1.11  % [INFO] 	 Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ... 
% 1.54/1.16  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 0 axioms). 
% 1.80/1.20  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.80/1.20  % [INFO] 	 Type checking passed. 
% 1.80/1.20  % [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 ... 
% 89.34/15.86  % [INFO] 	 Killing All external provers ... 
% 89.55/15.86  % Time passed: 15454ms (effective reasoning time: 15027ms)
% 89.55/15.87  % Axioms used in derivation (5): associative_commutative, normalization, premise_3, unfolding_2, premise_7
% 89.55/15.87  % No. of inferences in proof: 38
% 89.55/15.87  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 15454 ms resp. 15027 ms w/o parsing
% 89.55/15.91  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 89.55/15.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------