TSTP Solution File: SWW400-1 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW400-1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n002.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 18:25:04 EDT 2024

% Result   : Unsatisfiable 75.08s 12.90s
% Output   : Refutation 75.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   48 (  28 unt;   0 typ;   0 def)
%            Number of atoms       :   79 (  40 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  497 (  33   ~;  27   |;   0   &; 437   @)
%                                         (   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   :  102 (   0   ^ 102   !;   0   ?; 102   :)

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

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

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

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

thf(2,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(18,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(19,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ A @ ( sep @ B @ C ) )
      = ( sep @ B @ ( sep @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[18]) ).

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

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(lifteq,[status(thm)],[20]) ).

thf(87,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sep @ B @ ( sep @ A @ C ) )
        = E )
      | ( ( sep @ A @ ( sep @ B @ C ) )
       != ( sep @ ( lseg @ D @ D ) @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[19,21]) ).

thf(88,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
      = ( sep @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( lseg @ G @ G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( G )),bind(E,$thf( sep @ H @ I ))]]) ).

thf(141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ B @ ( sep @ ( lseg @ A @ A ) @ C ) )
      = ( sep @ B @ C ) ),
    inference(simp,[status(thm)],[88]) ).

thf(218,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)],[141,21]) ).

thf(219,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = ( sep @ ( lseg @ C @ C ) @ B ) ),
    inference(pattern_uni,[status(thm)],[218:[bind(A,$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(280,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = ( sep @ ( lseg @ C @ C ) @ B ) ),
    inference(simp,[status(thm)],[219]) ).

thf(8665,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)],[280,21]) ).

thf(8666,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ B @ B ) @ A )
      = A ),
    inference(pattern_uni,[status(thm)],[8665:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).

thf(9175,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ B @ B ) @ A )
      = A ),
    inference(simp,[status(thm)],[8666]) ).

thf(15,axiom,
    heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).

thf(51,plain,
    heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ A @ ( sep @ B @ C ) ) ) )
      | ( ( sep @ B @ ( sep @ A @ C ) )
       != ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ) ),
    inference(paramod_ordered,[status(thm)],[19,51]) ).

thf(130,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ A @ ( sep @ B @ C ) ) ) )
      | ( B
       != ( lseg @ x1 @ x2 ) )
      | ( ( sep @ A @ C )
       != emp ) ),
    inference(simp,[status(thm)],[114]) ).

thf(137,plain,
    ! [B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ A @ ( sep @ ( lseg @ x1 @ x2 ) @ B ) ) ) )
      | ( ( sep @ A @ B )
       != emp ) ),
    inference(simp,[status(thm)],[130]) ).

thf(29258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ C @ ( sep @ ( lseg @ x1 @ x2 ) @ D ) ) ) )
      | ( A != emp )
      | ( ( sep @ ( lseg @ B @ B ) @ A )
       != ( sep @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[9175,137]) ).

thf(29259,plain,
    ! [B: $i,A: $i] :
      ( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ B @ B ) @ ( sep @ ( lseg @ x1 @ x2 ) @ A ) ) ) )
      | ( A != emp ) ),
    inference(pattern_uni,[status(thm)],[29258:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( lseg @ F @ F )),bind(D,$thf( A ))]]) ).

thf(29597,plain,
    ! [A: $i] : ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ) ) ),
    inference(simp,[status(thm)],[29259]) ).

thf(9,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(35,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)],[9]) ).

thf(36,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)],[35]) ).

thf(37,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)],[36]) ).

thf(30425,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( heap @ ( sep @ ( lseg @ B @ D ) @ E ) )
      | ( ( heap @ ( sep @ ( next @ x2 @ nil ) @ ( sep @ ( lseg @ A @ A ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ) ) )
       != ( heap @ ( sep @ ( next @ B @ C ) @ ( sep @ ( lseg @ C @ D ) @ E ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29597,37]) ).

thf(30426,plain,
    ( ( x2 = nil )
    | ( heap @ ( sep @ ( lseg @ x2 @ nil ) @ ( sep @ ( lseg @ x1 @ x2 ) @ emp ) ) ) ),
    inference(pattern_uni,[status(thm)],[30425:[bind(A,$thf( nil )),bind(B,$thf( x2 )),bind(C,$thf( nil )),bind(D,$thf( nil )),bind(E,$thf( sep @ ( lseg @ x1 @ x2 ) @ emp ))]]) ).

thf(10,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/sandbox/benchmark/theBenchmark.p',unfolding_3) ).

thf(38,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)],[10]) ).

thf(39,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
      | ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) ) ),
    inference(cnf,[status(esa)],[38]) ).

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

thf(16,plain,
    ~ ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(17,plain,
    ~ ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ),
    inference(polarity_switch,[status(thm)],[16]) ).

thf(7506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ A @ B ) @ ( sep @ ( lseg @ B @ nil ) @ C ) ) )
      | ( ( heap @ ( sep @ ( lseg @ A @ nil ) @ C ) )
       != ( heap @ ( sep @ ( lseg @ x1 @ nil ) @ emp ) ) ) ),
    inference(paramod_ordered,[status(thm)],[39,17]) ).

thf(7507,plain,
    ! [A: $i] :
      ~ ( heap @ ( sep @ ( lseg @ x1 @ A ) @ ( sep @ ( lseg @ A @ nil ) @ emp ) ) ),
    inference(pattern_uni,[status(thm)],[7506:[bind(A,$thf( x1 )),bind(B,$thf( B )),bind(C,$thf( emp ))]]) ).

thf(7640,plain,
    ! [A: $i] :
      ~ ( heap @ ( sep @ ( lseg @ x1 @ A ) @ ( sep @ ( lseg @ A @ nil ) @ emp ) ) ),
    inference(simp,[status(thm)],[7507]) ).

thf(7841,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ B @ ( sep @ A @ C ) ) )
      | ( ( sep @ A @ ( sep @ B @ C ) )
       != ( sep @ ( lseg @ x1 @ D ) @ ( sep @ ( lseg @ D @ nil ) @ emp ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19,7640]) ).

thf(7842,plain,
    ! [A: $i] :
      ~ ( heap @ ( sep @ ( lseg @ A @ nil ) @ ( sep @ ( lseg @ x1 @ A ) @ emp ) ) ),
    inference(pattern_uni,[status(thm)],[7841:[bind(A,$thf( lseg @ x1 @ G )),bind(B,$thf( lseg @ G @ nil )),bind(C,$thf( emp )),bind(D,$thf( G ))]]) ).

thf(7875,plain,
    ! [A: $i] :
      ~ ( heap @ ( sep @ ( lseg @ A @ nil ) @ ( sep @ ( lseg @ x1 @ A ) @ emp ) ) ),
    inference(simp,[status(thm)],[7842]) ).

thf(32324,plain,
    ( ( x2 = nil )
    | $false ),
    inference(rewrite,[status(thm)],[30426,7875]) ).

thf(32325,plain,
    x2 = nil,
    inference(simp,[status(thm)],[32324]) ).

thf(14,axiom,
    nil != x2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_2) ).

thf(48,plain,
    nil != x2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(49,plain,
    nil != x2,
    inference(polarity_switch,[status(thm)],[48]) ).

thf(50,plain,
    x2 != nil,
    inference(lifteq,[status(thm)],[49]) ).

thf(32326,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[32325,50]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW400-1 : TPTP v8.2.0. Released v5.2.0.
% 0.00/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n002.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 07:03:40 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.82/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.97  % [INFO] 	 Parsing done (112ms). 
% 1.20/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.71/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ... 
% 1.88/1.26  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 1.88/1.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.88/1.29  % [INFO] 	 Type checking passed. 
% 1.88/1.29  % [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 ... 
% 75.08/12.89  % [INFO] 	 Killing All external provers ... 
% 75.08/12.90  % Time passed: 12372ms (effective reasoning time: 11914ms)
% 75.08/12.90  % Axioms used in derivation (6): premise_2, associative_commutative, normalization, unfolding_3, premise_3, unfolding_2
% 75.08/12.90  % No. of inferences in proof: 48
% 75.08/12.90  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 12372 ms resp. 11914 ms w/o parsing
% 75.08/12.93  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 75.08/12.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------