TSTP Solution File: LCL429-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LCL429-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 11:30:21 EDT 2023

% Result   : Unsatisfiable 2.71s 1.59s
% Output   : Refutation 2.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   34 (  11 unt;  17 typ;   0 def)
%            Number of atoms       :   29 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  408 (  14   ~;  12   |;   0   &; 382   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  14 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  17 usr;   8 con; 0-3 aty)
%            Number of variables   :   54 (   0   ^;  54   !;   0   ?;  54   :)

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

thf(v_p_type,type,
    v_p: $i ).

thf(c_PropLog_Othms_type,type,
    c_PropLog_Othms: $i > $i > $i ).

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

thf(c_PropLog_Ohyps_type,type,
    c_PropLog_Ohyps: $i > $i > $i > $i ).

thf(t_a_type,type,
    t_a: $i ).

thf(v_F_type,type,
    v_F: $i ).

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

thf(tc_PropLog_Opl_type,type,
    tc_PropLog_Opl: $i > $i ).

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

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

thf(c_PropLog_Opl_Ovar_type,type,
    c_PropLog_Opl_Ovar: $i > $i > $i ).

thf(v_v_type,type,
    v_v: $i ).

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

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

thf(c_PropLog_Opl_Oop_A_N_62_type,type,
    c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).

thf(c_PropLog_Opl_Ofalse_type,type,
    c_PropLog_Opl_Ofalse: $i ).

thf(2,negated_conjecture,
    ~ ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ v_t @ t_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ v_v @ t_a ) @ v_F @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(10,plain,
    ~ ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ v_t @ t_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ v_v @ t_a ) @ v_F @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ A @ ( c_minus @ B @ ( c_insert @ C @ c_emptyset @ D ) @ ( tc_set @ D ) ) @ D ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ C @ D ) @ c_PropLog_Opl_Ofalse @ D ) @ ( c_minus @ ( c_PropLog_Ohyps @ A @ B @ D ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ C @ D ) @ c_emptyset @ ( tc_PropLog_Opl @ D ) ) @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ ( tc_PropLog_Opl @ D ) ) @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ohyps__Diff_0) ).

thf(14,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ A @ ( c_minus @ B @ ( c_insert @ C @ c_emptyset @ D ) @ ( tc_set @ D ) ) @ D ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ C @ D ) @ c_PropLog_Opl_Ofalse @ D ) @ ( c_minus @ ( c_PropLog_Ohyps @ A @ B @ D ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ C @ D ) @ c_emptyset @ ( tc_PropLog_Opl @ D ) ) @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ ( tc_PropLog_Opl @ D ) ) @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1,negated_conjecture,
    ! [A: $i] : ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ A @ t_a ) @ v_F @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(9,plain,
    ! [A: $i] : ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ A @ t_a ) @ v_F @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_insert @ B @ C @ ( tc_PropLog_Opl @ D ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
      | ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ c_PropLog_Opl_Ofalse @ D ) @ C @ ( tc_PropLog_Opl @ D ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ C @ D ) @ ( tc_PropLog_Opl @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms__excluded__middle__rule_0) ).

thf(17,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_insert @ B @ C @ ( tc_PropLog_Opl @ D ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
      | ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ c_PropLog_Opl_Ofalse @ D ) @ C @ ( tc_PropLog_Opl @ D ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ C @ D ) @ ( tc_PropLog_Opl @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(3,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_minus @ B @ C @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ ( c_minus @ E @ C @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ D ) @ ( tc_PropLog_Opl @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_ODiff__weaken__left_0) ).

thf(12,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_minus @ B @ C @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ ( c_minus @ E @ C @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ D ) @ ( tc_PropLog_Opl @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ C @ c_emptyset @ D ) @ ( tc_set @ D ) ) @ D ) @ E @ ( tc_set @ D ) ) @ ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ C @ E @ D ) @ ( tc_set @ D ) ) @ D ) @ ( tc_set @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__subset2_0) ).

thf(16,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ C @ c_emptyset @ D ) @ ( tc_set @ D ) ) @ D ) @ E @ ( tc_set @ D ) ) @ ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ C @ E @ D ) @ ( tc_set @ D ) ) @ D ) @ ( tc_set @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ ( tc_PropLog_Opl @ C ) ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left_0) ).

thf(19,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ ( tc_PropLog_Opl @ C ) ) )
      | ( c_in @ A @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ ( c_insert @ D @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ C ) @ ( tc_set @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__same_0) ).

thf(15,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ ( c_insert @ D @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ C ) @ ( tc_set @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(21,plain,
    $false,
    inference(e,[status(thm)],[10,14,9,17,12,16,19,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL429-2 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 15:06:31 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.94/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.95  % [INFO] 	 Parsing done (117ms). 
% 1.22/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.15  % [INFO] 	 eprover registered as external prover. 
% 1.64/1.15  % [INFO] 	 cvc4 registered as external prover. 
% 1.64/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.22  % [INFO] 	 Found a conjecture and 6 axioms. Running axiom selection ... 
% 1.86/1.24  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 1.94/1.27  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.94/1.27  % [INFO] 	 Type checking passed. 
% 1.94/1.27  % [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 ... 
% 2.71/1.59  % External prover 'e' found a proof!
% 2.71/1.59  % [INFO] 	 Killing All external provers ... 
% 2.71/1.59  % Time passed: 1078ms (effective reasoning time: 631ms)
% 2.71/1.59  % 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)>
% 2.71/1.59  % Axioms used in derivation (6): cls_PropLog_Oinsert__Diff__subset2_0, cls_PropLog_Oweaken__left_0, cls_PropLog_ODiff__weaken__left_0, cls_PropLog_Othms__excluded__middle__rule_0, cls_PropLog_Oinsert__Diff__same_0, cls_PropLog_Ohyps__Diff_0
% 2.71/1.59  % No. of inferences in proof: 17
% 2.71/1.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1078 ms resp. 631 ms w/o parsing
% 2.71/1.63  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.71/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------