TSTP Solution File: PUZ062-2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : PUZ062-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Tue May 21 02:26:46 EDT 2024

% Result   : Unsatisfiable 3.26s 1.72s
% Output   : Refutation 3.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   48 (  17 unt;  21 typ;   0 def)
%            Number of atoms       :   41 (  12 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  386 (  16   ~;  14   |;   0   &; 356   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  21 usr;  12 con; 0-4 aty)
%            Number of variables   :   40 (   0   ^  40   !;   0   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_in_type,type,
    c_in: $i > $i > $i > $o ).

thf(v_t_type,type,
    v_t: $i ).

thf(c_Mutil_Otiling_type,type,
    c_Mutil_Otiling: $i > $i > $i ).

thf(c_Mutil_Odomino_type,type,
    c_Mutil_Odomino: $i ).

thf(tc_prod_type,type,
    tc_prod: $i > $i > $i ).

thf(tc_nat_type,type,
    tc_nat: $i ).

thf(tc_set_type,type,
    tc_set: $i > $i ).

thf(c_Finite__Set_Ocard_type,type,
    c_Finite__Set_Ocard: $i > $i > $i ).

thf(c_inter_type,type,
    c_inter: $i > $i > $i > $i ).

thf(c_Mutil_Ocoloured_type,type,
    c_Mutil_Ocoloured: $i > $i ).

thf(c_0_type,type,
    c_0: $i ).

thf(c_Suc_type,type,
    c_Suc: $i > $i ).

thf(v_a_type,type,
    v_a: $i ).

thf(c_emptyset_type,type,
    c_emptyset: $i ).

thf(c_insert_type,type,
    c_insert: $i > $i > $i > $i ).

thf(c_Pair_type,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(v_i_type,type,
    v_i: $i ).

thf(v_j_type,type,
    v_j: $i ).

thf(v_m_type,type,
    v_m: $i ).

thf(v_n_type,type,
    v_n: $i ).

thf(c_Finite__Set_OFinites_type,type,
    c_Finite__Set_OFinites: $i ).

thf(12,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

thf(37,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(5,negated_conjecture,
    ( ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
    = ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(14,plain,
    ( ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
    = ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,negated_conjecture,
    ( ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
    = ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(17,plain,
    ( ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
    = ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).

thf(35,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(3,negated_conjecture,
    ( ( c_inter @ v_a @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) )
    = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(18,plain,
    ( ( c_inter @ v_a @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) )
    = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ C @ A @ B )
      | ( ( c_Finite__Set_Ocard @ ( c_insert @ C @ A @ B ) @ B )
        = ( c_Suc @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
      | ( c_in @ C @ A @ B )
      | ( ( c_Finite__Set_Ocard @ ( c_insert @ C @ A @ B ) @ B )
        = ( c_Suc @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(4,negated_conjecture,
    ( ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
    = ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(19,plain,
    ( ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
    = ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,negated_conjecture,
    c_in @ v_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(15,plain,
    c_in @ v_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

thf(38,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).

thf(33,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,negated_conjecture,
    ( ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
   != ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(16,plain,
    ( ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
   != ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ~ ( c_in @ A @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).

thf(31,plain,
    ! [A: $i] :
      ( ~ ( c_in @ A @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
      | ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(43,plain,
    $false,
    inference(e,[status(thm)],[37,14,29,17,35,18,26,19,15,38,33,16,31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : PUZ062-2 : TPTP v8.2.0. Released v3.2.0.
% 0.16/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n002.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Sat May 18 10:42:39 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.97  % [INFO] 	 Parsing done (106ms). 
% 1.34/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 1.93/1.27  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.93/1.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.93/1.29  % [INFO] 	 Type checking passed. 
% 1.93/1.29  % [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 ... 
% 3.26/1.72  % External prover 'e' found a proof!
% 3.26/1.72  % [INFO] 	 Killing All external provers ... 
% 3.26/1.72  % Time passed: 1189ms (effective reasoning time: 734ms)
% 3.26/1.72  % Axioms used in derivation (7): cls_Set_OInt__iff_2, cls_Finite__Set_Ocard__insert__disjoint_0, cls_Set_Oinsert__iff_1, cls_Mutil_Otiling__domino__finite_0, cls_Set_OInt__iff_1, cls_Finite__Set_Ofinite__Int_1, cls_Set_Oempty__iff_0
% 3.26/1.72  % No. of inferences in proof: 27
% 3.26/1.72  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1189 ms resp. 734 ms w/o parsing
% 3.26/1.75  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.26/1.75  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------