TSTP Solution File: SWW443-1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW443-1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Fri May 19 12:23:54 EDT 2023

% Result   : Unsatisfiable 74.37s 24.24s
% Output   : Refutation 74.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   96 (  56 unt;  25 typ;   0 def)
%            Number of atoms       :   92 (  61 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  433 (  63   ~;  21   |;   0   &; 349   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  25 usr;  23 con; 0-2 aty)
%            Number of variables   :   76 (   0   ^;  76   !;   0   ?;  76   :)

% Comments : 
%------------------------------------------------------------------------------
thf(x1_type,type,
    x1: $i ).

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

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

thf(x4_type,type,
    x4: $i ).

thf(x19_type,type,
    x19: $i ).

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

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

thf(x8_type,type,
    x8: $i ).

thf(x11_type,type,
    x11: $i ).

thf(x15_type,type,
    x15: $i ).

thf(x14_type,type,
    x14: $i ).

thf(x16_type,type,
    x16: $i ).

thf(x13_type,type,
    x13: $i ).

thf(x5_type,type,
    x5: $i ).

thf(x6_type,type,
    x6: $i ).

thf(x17_type,type,
    x17: $i ).

thf(x18_type,type,
    x18: $i ).

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

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

thf(x9_type,type,
    x9: $i ).

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

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

thf(x10_type,type,
    x10: $i ).

thf(x12_type,type,
    x12: $i ).

thf(x7_type,type,
    x7: $i ).

thf(13,axiom,
    x17 != x18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_7) ).

thf(69,plain,
    x17 != x18,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(32,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(120,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)],[32]) ).

thf(21,axiom,
    x8 != x9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_13) ).

thf(92,plain,
    x8 != x9,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(35,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(129,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)],[35]) ).

thf(26,axiom,
    x1 != x15,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_18) ).

thf(105,plain,
    x1 != x15,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(5,axiom,
    x11 != x15,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_4) ).

thf(45,plain,
    x11 != x15,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(33,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/sandbox/benchmark/theBenchmark.p',wellformedness_5) ).

thf(123,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)],[33]) ).

thf(14,axiom,
    x3 != x5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_6) ).

thf(72,plain,
    x3 != x5,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(15,axiom,
    x11 != x16,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_2) ).

thf(75,plain,
    x11 != x16,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(34,axiom,
    x1 != x6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_16) ).

thf(126,plain,
    x1 != x6,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(4,axiom,
    x2 != x8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_8) ).

thf(42,plain,
    x2 != x8,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2,axiom,
    x4 != x19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_15) ).

thf(37,plain,
    x4 != x19,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,axiom,
    x5 != x15,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_22) ).

thf(57,plain,
    x5 != x15,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(16,axiom,
    x13 != x19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_20) ).

thf(78,plain,
    x13 != x19,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(20,axiom,
    x14 != x18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_11) ).

thf(89,plain,
    x14 != x18,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(30,axiom,
    heap @ ( sep @ ( lseg @ x10 @ x1 ) @ ( sep @ ( lseg @ x18 @ x15 ) @ ( sep @ ( lseg @ x1 @ x14 ) @ ( sep @ ( lseg @ x1 @ x3 ) @ ( sep @ ( lseg @ x12 @ x13 ) @ ( sep @ ( lseg @ x2 @ x5 ) @ ( sep @ ( lseg @ x2 @ x12 ) @ ( sep @ ( lseg @ x2 @ x18 ) @ ( sep @ ( lseg @ x2 @ x8 ) @ ( sep @ ( lseg @ x9 @ x5 ) @ ( sep @ ( lseg @ x7 @ x5 ) @ ( sep @ ( lseg @ x11 @ x9 ) @ ( sep @ ( lseg @ x11 @ x7 ) @ emp ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_23) ).

thf(116,plain,
    heap @ ( sep @ ( lseg @ x10 @ x1 ) @ ( sep @ ( lseg @ x18 @ x15 ) @ ( sep @ ( lseg @ x1 @ x14 ) @ ( sep @ ( lseg @ x1 @ x3 ) @ ( sep @ ( lseg @ x12 @ x13 ) @ ( sep @ ( lseg @ x2 @ x5 ) @ ( sep @ ( lseg @ x2 @ x12 ) @ ( sep @ ( lseg @ x2 @ x18 ) @ ( sep @ ( lseg @ x2 @ x8 ) @ ( sep @ ( lseg @ x9 @ x5 ) @ ( sep @ ( lseg @ x7 @ x5 ) @ ( sep @ ( lseg @ x11 @ x9 ) @ ( sep @ ( lseg @ x11 @ x7 ) @ emp ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(10,axiom,
    x2 != x13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_9) ).

thf(60,plain,
    x2 != x13,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(31,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/sandbox/benchmark/theBenchmark.p',unfolding_5) ).

thf(117,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)],[31]) ).

thf(8,axiom,
    x11 != x13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).

thf(54,plain,
    x11 != x13,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(19,axiom,
    x4 != x18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_14) ).

thf(86,plain,
    x4 != x18,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).

thf(81,plain,
    ! [B: $i,A: $i] :
      ( ( sep @ ( lseg @ A @ A ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(23,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/sandbox/benchmark/theBenchmark.p',unfolding_4) ).

thf(98,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)],[23]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_1) ).

thf(103,plain,
    ! [B: $i,A: $i] :
      ~ ( heap @ ( sep @ ( next @ nil @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(12,axiom,
    x6 != x13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_1) ).

thf(66,plain,
    x6 != x13,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
      | ( A = nil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_2) ).

thf(108,plain,
    ! [B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( lseg @ nil @ A ) @ B ) )
      | ( A = nil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(6,axiom,
    x2 != x14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_10) ).

thf(48,plain,
    x2 != x14,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(11,axiom,
    x5 != x16,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_21) ).

thf(63,plain,
    x5 != x16,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(22,axiom,
    x1 != x14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_19) ).

thf(95,plain,
    x1 != x14,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

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(40,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(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( next @ A @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_3) ).

thf(114,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)],[29]) ).

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

thf(36,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,axiom,
    x14 != x16,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_12) ).

thf(51,plain,
    x14 != x16,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( heap @ ( sep @ ( next @ A @ B ) @ ( sep @ ( lseg @ A @ C ) @ D ) ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_4) ).

thf(111,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)],[28]) ).

thf(18,axiom,
    x3 != x4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_5) ).

thf(83,plain,
    x3 != x4,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(24,axiom,
    x1 != x13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_17) ).

thf(100,plain,
    x1 != x13,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(17453,plain,
    $false,
    inference(cvc4,[status(thm)],[69,120,92,129,105,45,123,72,75,126,42,37,57,78,89,116,60,117,54,86,81,98,103,66,108,48,63,95,40,114,36,51,111,83,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWW443-1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n028.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 22:44:04 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 1.05/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.43/1.10  % [INFO] 	 Parsing done (187ms). 
% 1.43/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.87/1.34  % [INFO] 	 eprover registered as external prover. 
% 1.87/1.35  % [INFO] 	 cvc4 registered as external prover. 
% 1.87/1.35  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.42  % [INFO] 	 Found a conjecture and 34 axioms. Running axiom selection ... 
% 2.24/1.47  % [INFO] 	 Axiom selection finished. Selected 34 axioms (removed 0 axioms). 
% 2.32/1.50  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.32/1.51  % [INFO] 	 Type checking passed. 
% 2.32/1.51  % [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 ... 
% 74.37/24.24  % External prover 'cvc4' found a proof!
% 74.37/24.24  % [INFO] 	 Killing All external provers ... 
% 74.37/24.24  % Time passed: 23721ms (effective reasoning time: 23112ms)
% 74.37/24.24  % 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)>
% 74.37/24.24  % Axioms used in derivation (34): premise_20, wellformedness_2, premise_6, premise_23, premise_15, wellformedness_3, premise_12, premise_16, premise_11, premise_18, premise_1, premise_4, wellformedness_1, premise_7, premise_5, premise_19, premise_14, premise_2, wellformedness_5, premise_13, associative_commutative, unfolding_5, normalization, premise_9, unfolding_3, unfolding_4, premise_22, wellformedness_4, premise_8, premise_3, unfolding_2, premise_17, premise_21, premise_10
% 74.37/24.24  % No. of inferences in proof: 71
% 74.37/24.24  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23721 ms resp. 23112 ms w/o parsing
% 74.79/24.29  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 74.79/24.29  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------