TSTP Solution File: SWV284-2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWV284-2 : 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 05:51:06 EDT 2024

% Result   : Unsatisfiable 7.15s 2.45s
% Output   : Refutation 7.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   49 (  14 unt;  15 typ;   0 def)
%            Number of atoms       :   66 (   6 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  416 (  30   ~;  20   |;   0   &; 366   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :   68 (   0   ^  68   !;   0   ?;  68   :)

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

thf(v_x_type,type,
    v_x: $i > $i ).

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

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

thf(c_Message_Omsg_ONonce_type,type,
    c_Message_Omsg_ONonce: $i > $i ).

thf(c_Event_Oused_type,type,
    c_Event_Oused: $i > $i ).

thf(v_list_type,type,
    v_list: $i ).

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

thf(v_N_type,type,
    v_N: $i ).

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

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

thf(v_msg_type,type,
    v_msg: $i ).

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

thf(v_sko__upX_type,type,
    v_sko__upX: $i > $i ).

thf(c_plus_type,type,
    c_plus: $i > $i > $i > $i ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(9,plain,
    ! [A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,plain,
    ! [A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(1,negated_conjecture,
    ! [A: $i] : ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(7,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_0) ).

thf(14,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(53,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ C @ D @ tc_nat )
      | ( ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat )
       != ( c_lessequals @ ( c_plus @ B @ C @ tc_nat ) @ D @ tc_nat ) ) ),
    inference(paramod_ordered,[status(thm)],[7,15]) ).

thf(54,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ B @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat ),
    inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( c_plus @ I @ J @ tc_nat )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( v_x @ ( c_plus @ I @ J @ tc_nat ) ))]]) ).

thf(55,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ B @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat ),
    inference(simp,[status(thm)],[54]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ ( v_sko__upX @ B ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg__Nonce__supply_0) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ ( v_sko__upX @ B ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ ( v_sko__upX @ B ) @ A @ tc_nat ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(59,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Message_Oparts @ ( c_insert @ D @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ( ( c_lessequals @ B @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat )
       != ( c_lessequals @ ( v_sko__upX @ D ) @ C @ tc_nat ) ) ),
    inference(paramod_ordered,[status(thm)],[55,13]) ).

thf(60,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ B ) @ tc_nat ) ) ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ),
    inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( G )),bind(B,$thf( v_sko__upX @ J )),bind(C,$thf( v_x @ ( c_plus @ G @ ( v_sko__upX @ J ) @ tc_nat ) )),bind(D,$thf( J ))]]) ).

thf(67,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ B ) @ tc_nat ) ) ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ),
    inference(simp,[status(thm)],[60]) ).

thf(187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
      | ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
       != ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ B @ ( v_sko__upX @ C ) @ tc_nat ) ) ) @ ( c_Message_Oparts @ ( c_insert @ C @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(paramod_ordered,[status(thm)],[11,67]) ).

thf(188,plain,
    ! [A: $i] : ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ v_msg ) @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ),
    inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( c_plus @ D @ ( v_sko__upX @ v_msg ) @ tc_nat )),bind(B,$thf( D )),bind(C,$thf( v_msg ))]]) ).

thf(191,plain,
    ! [A: $i] : ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ v_msg ) @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ),
    inference(simp,[status(thm)],[188]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( c_lessequals @ A @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_1) ).

thf(16,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( c_lessequals @ A @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(17,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( c_lessequals @ A @ C @ tc_nat ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(92,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ B @ D @ tc_nat )
      | ( ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat )
       != ( c_lessequals @ ( c_plus @ B @ C @ tc_nat ) @ D @ tc_nat ) ) ),
    inference(paramod_ordered,[status(thm)],[7,17]) ).

thf(93,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat ),
    inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( c_plus @ I @ J @ tc_nat )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( v_x @ ( c_plus @ I @ J @ tc_nat ) ))]]) ).

thf(97,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat ),
    inference(simp,[status(thm)],[93]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ v_N @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ v_N @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    ! [A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ v_N @ A @ tc_nat ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(99,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
      | ( ( c_lessequals @ A @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat )
       != ( c_lessequals @ v_N @ C @ tc_nat ) ) ),
    inference(paramod_ordered,[status(thm)],[97,10]) ).

thf(100,plain,
    ! [A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ v_N @ A @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ),
    inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( v_N )),bind(B,$thf( F )),bind(C,$thf( v_x @ ( c_plus @ v_N @ F @ tc_nat ) ))]]) ).

thf(109,plain,
    ! [A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ v_N @ A @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ),
    inference(simp,[status(thm)],[100]) ).

thf(209,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ v_msg ) @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
     != ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ v_N @ B @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ) ),
    inference(paramod_ordered,[status(thm)],[191,109]) ).

thf(210,plain,
    $false,
    inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( v_N )),bind(B,$thf( v_sko__upX @ v_msg ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV284-2 : TPTP v8.2.0. Released v3.2.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.35  % Computer : n006.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 07:48:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.96  % [INFO] 	 Parsing done (101ms). 
% 1.20/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.61/1.17  % [INFO] 	 nitpick registered as external prover. 
% 1.61/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.79/1.26  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.79/1.27  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.79/1.27  % [INFO] 	 Type checking passed. 
% 1.79/1.27  % [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 ... 
% 7.15/2.44  % [INFO] 	 Killing All external provers ... 
% 7.15/2.45  % Time passed: 1923ms (effective reasoning time: 1477ms)
% 7.15/2.45  % Axioms used in derivation (3): cls_Nat_Oadd__leE_0, cls_Message_Omsg__Nonce__supply_0, cls_Nat_Oadd__leE_1
% 7.15/2.45  % No. of inferences in proof: 34
% 7.15/2.45  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1923 ms resp. 1477 ms w/o parsing
% 7.15/2.48  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.15/2.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------