TSTP Solution File: SWW421-1 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW421-1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n028.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 18:25:07 EDT 2024

% Result   : Unsatisfiable 95.00s 15.90s
% Output   : Refutation 95.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   47 (  29 unt;   0 typ;   0 def)
%            Number of atoms       :   74 (  44 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  482 (  25   ~;  25   |;   0   &; 432   @)
%                                         (   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   :  105 (   0   ^ 105   !;   0   ?; 105   :)

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

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

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

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

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

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normalization) ).

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

thf(47,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(lifteq,[status(thm)],[46]) ).

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(19,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(20,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[19]) ).

thf(164,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( sep @ D @ ( sep @ C @ E ) ) )
      | ( ( sep @ ( lseg @ A @ A ) @ B )
       != ( sep @ C @ ( sep @ D @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47,20]) ).

thf(165,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
      = ( sep @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( G )),bind(B,$thf( sep @ H @ I )),bind(C,$thf( lseg @ G @ G )),bind(D,$thf( H )),bind(E,$thf( I ))]]) ).

thf(215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
      = ( sep @ B @ C ) ),
    inference(simp,[status(thm)],[165]) ).

thf(862,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sep @ B @ C )
        = E )
      | ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
       != ( sep @ ( lseg @ D @ D ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[215,47]) ).

thf(863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = ( sep @ ( lseg @ C @ C ) @ B ) ),
    inference(pattern_uni,[status(thm)],[862:[bind(A,$thf( K )),bind(B,$thf( lseg @ G @ G )),bind(C,$thf( I )),bind(D,$thf( G )),bind(E,$thf( sep @ ( lseg @ K @ K ) @ I ))]]) ).

thf(895,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = ( sep @ ( lseg @ C @ C ) @ B ) ),
    inference(simp,[status(thm)],[863]) ).

thf(10982,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sep @ ( lseg @ C @ C ) @ B )
        = E )
      | ( ( sep @ ( lseg @ A @ A ) @ B )
       != ( sep @ ( lseg @ D @ D ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[895,47]) ).

thf(10983,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ B @ B ) @ A )
      = A ),
    inference(pattern_uni,[status(thm)],[10982:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(11206,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ B @ B ) @ A )
      = A ),
    inference(simp,[status(thm)],[10983]) ).

thf(69,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)],[20,20]) ).

thf(70,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ C @ ( sep @ A @ D ) ) )
      = ( sep @ A @ ( sep @ B @ ( sep @ C @ D ) ) ) ),
    inference(pattern_uni,[status(thm)],[69:[bind(A,$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(113,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)],[70]) ).

thf(11,axiom,
    heap @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ ( next @ x1 @ x2 ) @ emp ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_4) ).

thf(42,plain,
    heap @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ ( next @ x1 @ x2 ) @ emp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(67,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ A @ ( sep @ B @ C ) ) ) )
      | ( ( sep @ B @ ( sep @ A @ C ) )
       != ( sep @ ( next @ x1 @ x2 ) @ emp ) ) ),
    inference(paramod_ordered,[status(thm)],[20,42]) ).

thf(100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ A @ ( sep @ B @ C ) ) ) )
      | ( B
       != ( next @ x1 @ x2 ) )
      | ( ( sep @ A @ C )
       != emp ) ),
    inference(simp,[status(thm)],[67]) ).

thf(126,plain,
    ! [B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ A @ ( sep @ ( next @ x1 @ x2 ) @ B ) ) ) )
      | ( ( sep @ A @ B )
       != emp ) ),
    inference(simp,[status(thm)],[100]) ).

thf(29414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ C @ ( sep @ ( next @ x1 @ x2 ) @ D ) ) ) )
      | ( B != emp )
      | ( ( sep @ ( lseg @ A @ A ) @ B )
       != ( sep @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[47,126]) ).

thf(29415,plain,
    ! [B: $i,A: $i] :
      ( ( heap @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ ( lseg @ B @ B ) @ ( sep @ ( next @ x1 @ x2 ) @ A ) ) ) )
      | ( A != emp ) ),
    inference(pattern_uni,[status(thm)],[29414:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( lseg @ F @ F )),bind(D,$thf( B ))]]) ).

thf(29618,plain,
    ! [A: $i] : ( heap @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( next @ x1 @ x2 ) @ emp ) ) ) ),
    inference(simp,[status(thm)],[29415]) ).

thf(31165,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 @ x2 @ x3 ) @ ( sep @ ( lseg @ E @ E ) @ ( sep @ ( next @ x1 @ x2 ) @ emp ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[113,29618]) ).

thf(31166,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x1 @ x2 ) @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ ( lseg @ A @ A ) @ emp ) ) ) ),
    inference(pattern_uni,[status(thm)],[31165:[bind(A,$thf( next @ x1 @ x2 )),bind(B,$thf( lseg @ x2 @ x3 )),bind(C,$thf( lseg @ I @ I )),bind(D,$thf( emp )),bind(E,$thf( I ))]]) ).

thf(31559,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x1 @ x2 ) @ ( sep @ ( lseg @ x2 @ x3 ) @ ( sep @ ( lseg @ A @ A ) @ emp ) ) ) ),
    inference(simp,[status(thm)],[31166]) ).

thf(39067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x1 @ x2 ) @ ( sep @ ( lseg @ x2 @ x3 ) @ A ) ) )
      | ( ( sep @ ( lseg @ B @ B ) @ A )
       != ( sep @ ( lseg @ C @ C ) @ emp ) ) ),
    inference(paramod_ordered,[status(thm)],[11206,31559]) ).

thf(39068,plain,
    heap @ ( sep @ ( next @ x1 @ x2 ) @ ( sep @ ( lseg @ x2 @ x3 ) @ emp ) ),
    inference(pattern_uni,[status(thm)],[39067:[bind(A,$thf( emp )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

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/sandbox2/benchmark/theBenchmark.p',unfolding_2) ).

thf(39,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(40,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)],[39]) ).

thf(41,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)],[40]) ).

thf(40094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( heap @ ( sep @ ( lseg @ A @ C ) @ D ) )
      | ( ( heap @ ( sep @ ( next @ x1 @ x2 ) @ ( sep @ ( lseg @ x2 @ x3 ) @ emp ) ) )
       != ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ B @ C ) @ D ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[39068,41]) ).

thf(40095,plain,
    ( ( x2 = x1 )
    | ( heap @ ( sep @ ( lseg @ x1 @ x3 ) @ emp ) ) ),
    inference(pattern_uni,[status(thm)],[40094:[bind(A,$thf( x1 )),bind(B,$thf( x2 )),bind(C,$thf( x3 )),bind(D,$thf( emp ))]]) ).

thf(1,negated_conjecture,
    ~ ( heap @ ( sep @ ( lseg @ x1 @ x3 ) @ emp ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_1) ).

thf(17,plain,
    ~ ( heap @ ( sep @ ( lseg @ x1 @ x3 ) @ emp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(18,plain,
    ~ ( heap @ ( sep @ ( lseg @ x1 @ x3 ) @ emp ) ),
    inference(polarity_switch,[status(thm)],[17]) ).

thf(41068,plain,
    ( ( x2 = x1 )
    | $false ),
    inference(rewrite,[status(thm)],[40095,18]) ).

thf(41069,plain,
    x2 = x1,
    inference(simp,[status(thm)],[41068]) ).

thf(7,axiom,
    x2 != x1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_2) ).

thf(32,plain,
    x2 != x1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(33,plain,
    x2 != x1,
    inference(polarity_switch,[status(thm)],[32]) ).

thf(34,plain,
    x2 != x1,
    inference(lifteq,[status(thm)],[33]) ).

thf(41070,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[41069,34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SWW421-1 : TPTP v8.2.0. Released v5.2.0.
% 0.08/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jun 19 08:27:55 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.00  % [INFO] 	 Parsing done (123ms). 
% 1.28/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.23  % [INFO] 	 nitpick registered as external prover. 
% 1.81/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ... 
% 2.08/1.33  % [INFO] 	 Axiom selection finished. Selected 15 axioms (removed 0 axioms). 
% 2.08/1.36  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.08/1.36  % [INFO] 	 Type checking passed. 
% 2.23/1.36  % [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 ... 
% 95.00/15.89  % [INFO] 	 Killing All external provers ... 
% 95.00/15.89  % Time passed: 15357ms (effective reasoning time: 14882ms)
% 95.00/15.90  % Axioms used in derivation (5): premise_2, associative_commutative, normalization, unfolding_2, premise_4
% 95.00/15.90  % No. of inferences in proof: 47
% 95.00/15.90  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15357 ms resp. 14882 ms w/o parsing
% 95.03/15.94  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 95.03/15.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------