TSTP Solution File: SWV282-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV282-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n031.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 12:14:45 EDT 2023

% Result   : Unsatisfiable 2.75s 1.68s
% Output   : Refutation 3.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   48 (  19 unt;  19 typ;   0 def)
%            Number of atoms       :   47 (  20 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  212 (  12   ~;  18   |;   0   &; 182   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;   8 con; 0-3 aty)
%            Number of variables   :   46 (   0   ^;  46   !;   0   ?;  46   :)

% Comments : 
%------------------------------------------------------------------------------
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_evs_H_H_type,type,
    v_evs_H_H: $i ).

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

thf(v_evs_H_type,type,
    v_evs_H: $i ).

thf(v_evs_type,type,
    v_evs: $i ).

thf(c_Binomial_Obinomial_type,type,
    c_Binomial_Obinomial: $i > $i > $i ).

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

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

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

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

thf(c_1_type,type,
    c_1: $i ).

thf(c_minus_type,type,
    c_minus: $i > $i > $i > $i ).

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

thf(c_less_type,type,
    c_less: $i > $i > $i > $o ).

thf(v_sko__urX_type,type,
    v_sko__urX: $i > $i ).

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

thf(c_SetInterval_OatMost_type,type,
    c_SetInterval_OatMost: $i > $i > $i ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_less @ A @ ( c_Suc @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc__eq__le_1) ).

thf(33,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_less @ A @ ( c_Suc @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ tc_nat )
      = ( c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).

thf(41,plain,
    ! [A: $i] :
      ( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ A @ tc_nat ) @ tc_nat )
      = ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(9,axiom,
    ! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).

thf(32,plain,
    ! [A: $i] : ( c_less @ A @ ( c_Suc @ A ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ c_0 )
      = c_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).

thf(22,plain,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ c_0 )
      = c_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ ( v_sko__urX @ B ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).

thf(39,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ ( v_sko__urX @ B ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).

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

thf(2,axiom,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ ( c_Suc @ c_0 ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).

thf(18,plain,
    ! [A: $i] :
      ( ( c_Binomial_Obinomial @ A @ ( c_Suc @ c_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add1_0) ).

thf(31,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_minus @ A @ B @ tc_nat )
       != c_0 )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_minus @ A @ B @ tc_nat )
       != c_0 )
      | ( c_lessequals @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1,negated_conjecture,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C = B )
      | ( A = C )
      | ( c_in @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( C = B )
      | ( A = C )
      | ( c_in @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(5,axiom,
    ( c_1
    = ( c_Suc @ c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).

thf(24,plain,
    ( c_1
    = ( c_Suc @ c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Binomial_Obinomial @ ( c_Suc @ A ) @ ( c_Suc @ B ) )
      = ( c_plus @ ( c_Binomial_Obinomial @ A @ B ) @ ( c_Binomial_Obinomial @ A @ ( c_Suc @ B ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ( c_Binomial_Obinomial @ ( c_Suc @ A ) @ ( c_Suc @ B ) )
      = ( c_plus @ ( c_Binomial_Obinomial @ A @ B ) @ ( c_Binomial_Obinomial @ A @ ( c_Suc @ B ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( c_minus @ A @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).

thf(29,plain,
    ! [A: $i] :
      ( ( c_minus @ A @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(43,plain,
    $false,
    inference(e,[status(thm)],[33,41,32,22,39,35,18,31,26,15,24,37,20,29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV282-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.35  % Computer : n031.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
% 0.16/0.35  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Fri May 19 02:57:11 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 1.00/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.09/1.00  % [INFO] 	 Parsing done (129ms). 
% 1.35/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.76/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.28  % [INFO] 	 Found a conjecture and 13 axioms. Running axiom selection ... 
% 1.76/1.30  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 2.04/1.32  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.04/1.32  % [INFO] 	 Type checking passed. 
% 2.04/1.32  % [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 ... 
% 2.75/1.68  % External prover 'e' found a proof!
% 2.75/1.68  % [INFO] 	 Killing All external provers ... 
% 2.75/1.68  % Time passed: 1172ms (effective reasoning time: 667ms)
% 2.75/1.68  % 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)>
% 2.75/1.68  % Axioms used in derivation (13): cls_Nat_Odiff__is__0__eq_0, cls_Nat_Onat__add__left__cancel__le_0, cls_Nat_Odiff__self__eq__0_0, cls_Nat_Ole__add1_0, cls_Nat_OOne__nat__def_0, cls_Binomial_Obinomial__1_0, cls_SetInterval_Ocard__atMost_0, cls_Nat_OlessI_0, cls_Public_ONonce__supply__lemma_0, cls_Binomial_Obinomial__Suc__Suc_0, cls_Nat_Oless__Suc__eq__le_1, cls_Binomial_Obinomial__n__0_0, cls_Nat_Onot__add__less2_0
% 2.75/1.68  % No. of inferences in proof: 29
% 2.75/1.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1172 ms resp. 667 ms w/o parsing
% 3.01/1.72  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.01/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------