TSTP Solution File: SWV261-2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWV261-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 05:44:14 EDT 2024

% Result   : Unsatisfiable 3.35s 2.11s
% Output   : Refutation 3.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   32 (   7 unt;  11 typ;   0 def)
%            Number of atoms       :   39 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  230 (  16   ~;  18   |;   0   &; 196   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :   52 (   0   ^  52   !;   0   ?;  52   :)

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

thf(v_X_type,type,
    v_X: $i ).

thf(v_G_type,type,
    v_G: $i ).

thf(tc_Message_Omsg_type,type,
    tc_Message_Omsg: $i ).

thf(c_lessequals_type,type,
    c_lessequals: $i > $i > $i > $o ).

thf(c_Message_Oparts_type,type,
    c_Message_Oparts: $i > $i ).

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

thf(v_H_type,type,
    v_H: $i ).

thf(c_union_type,type,
    c_union: $i > $i > $i > $i ).

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

thf(c_Main_OsubsetI__1_type,type,
    c_Main_OsubsetI__1: $i > $i > $i > $i ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(3,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un__subset2_0) ).

thf(14,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).

thf(17,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(2,negated_conjecture,
    ~ ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ v_G ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(12,plain,
    ~ ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ v_G ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1,negated_conjecture,
    c_in @ v_X @ v_G @ tc_Message_Omsg,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(11,plain,
    c_in @ v_X @ v_G @ tc_Message_Omsg,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ B @ C )
      | ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).

thf(19,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
      | ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__mono_0) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
      | ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ D @ A @ ( tc_set @ C ) )
      | ( c_lessequals @ D @ B @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).

thf(28,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
      | ~ ( c_lessequals @ D @ A @ ( tc_set @ C ) )
      | ( c_lessequals @ D @ B @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).

thf(21,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(33,plain,
    $false,
    inference(e,[status(thm)],[24,14,17,12,11,26,19,15,28,21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem  : SWV261-2 : TPTP v8.2.0. Released v3.2.0.
% 0.08/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n027.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.31  % CPULimit : 300
% 0.16/0.31  % WCLimit  : 300
% 0.16/0.31  % DateTime : Sun May 19 07:14:08 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.88/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/1.06  % [INFO] 	 Parsing done (152ms). 
% 1.28/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.41  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.41  % [INFO] 	 cvc4 registered as external prover. 
% 1.82/1.42  % [INFO] 	 Scanning for conjecture ... 
% 1.92/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 2.06/1.54  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 2.06/1.55  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.06/1.56  % [INFO] 	 Type checking passed. 
% 2.06/1.56  % [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 ... 
% 3.35/2.11  % External prover 'e' found a proof!
% 3.35/2.11  % [INFO] 	 Killing All external provers ... 
% 3.35/2.11  % Time passed: 1656ms (effective reasoning time: 1032ms)
% 3.35/2.11  % Axioms used in derivation (8): cls_Set_OsubsetI_1, cls_Set_OUnCI_1, cls_Set_OsubsetI_0, cls_Set_OinsertE_0, cls_Set_Osubset__trans_0, cls_Set_OUnCI_0, cls_Message_Oparts__mono_0, cls_Message_Oparts__Un__subset2_0
% 3.35/2.11  % No. of inferences in proof: 21
% 3.35/2.11  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1656 ms resp. 1032 ms w/o parsing
% 3.54/2.16  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.54/2.16  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------