TSTP Solution File: SWV247-2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWV247-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 05:44:04 EDT 2024

% Result   : Unsatisfiable 2.97s 1.63s
% Output   : Refutation 2.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   33 (   7 unt;  12 typ;   0 def)
%            Number of atoms       :   41 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  266 (  18   ~;  20   |;   0   &; 228   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :   44 (   0   ^  44   !;   0   ?;  44   :)

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

thf(c_Message_Omsg_OCrypt_type,type,
    c_Message_Omsg_OCrypt: $i > $i > $i ).

thf(v_K_type,type,
    v_K: $i ).

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

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

thf(c_Message_Oanalz_type,type,
    c_Message_Oanalz: $i > $i ).

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

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

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

thf(c_Message_Osynth_type,type,
    c_Message_Osynth: $i > $i ).

thf(c_Message_Omsg_OKey_type,type,
    c_Message_Omsg_OKey: $i > $i ).

thf(c_Message_OinvKey_type,type,
    c_Message_OinvKey: $i > $i ).

thf(9,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(25,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)],[9]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).

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

thf(3,negated_conjecture,
    ~ ( c_in @ v_X @ ( c_union @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ v_G ) @ tc_Message_Omsg ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(13,plain,
    ~ ( c_in @ v_X @ ( c_union @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ v_G ) @ tc_Message_Omsg ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).

thf(17,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).

thf(27,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(2,negated_conjecture,
    c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ v_K ) ) @ ( c_union @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ v_G ) @ tc_Message_Omsg ) @ tc_Message_Omsg,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(12,plain,
    c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ v_K ) ) @ ( c_union @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ v_G ) @ tc_Message_Omsg ) @ tc_Message_Omsg,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1,negated_conjecture,
    c_in @ ( c_Message_Omsg_OCrypt @ v_K @ v_X ) @ ( c_union @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ v_G ) @ tc_Message_Omsg ) @ tc_Message_Omsg,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(11,plain,
    c_in @ ( c_Message_Omsg_OCrypt @ v_K @ v_X ) @ ( c_union @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ v_G ) @ tc_Message_Omsg ) @ tc_Message_Omsg,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(8,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(23,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)],[8]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth_0) ).

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

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(32,plain,
    $false,
    inference(cvc4,[status(thm)],[25,21,13,17,27,12,11,23,19,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV247-2 : TPTP v8.2.0. Released v3.2.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun May 19 08:28:39 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.97/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/0.96  % [INFO] 	 Parsing done (97ms). 
% 1.21/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.68/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.68/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.86/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 1.86/1.27  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.86/1.29  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.86/1.29  % [INFO] 	 Type checking passed. 
% 1.86/1.29  % [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 ... 
% 2.68/1.62  % External prover 'cvc4' found a proof!
% 2.97/1.62  % [INFO] 	 Killing All external provers ... 
% 2.97/1.62  % Time passed: 1099ms (effective reasoning time: 648ms)
% 2.97/1.63  % Axioms used in derivation (7): cls_Message_Oanalz_OInj_0, cls_Set_OUnCI_1, cls_Message_OCrypt__synth_1, cls_Set_OUnE_0, cls_Set_OUnCI_0, cls_Message_OKey__synth_0, cls_Message_Oanalz_ODecrypt__dest_0
% 2.97/1.63  % No. of inferences in proof: 21
% 2.97/1.63  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1099 ms resp. 648 ms w/o parsing
% 2.97/1.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.97/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------