TSTP Solution File: SET858-2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET858-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 03:04:18 EDT 2024

% Result   : Unsatisfiable 2.53s 1.50s
% Output   : Refutation 2.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   33 (  11 unt;  10 typ;   0 def)
%            Number of atoms       :   67 (   4 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  500 (  34   ~;  44   |;   0   &; 422   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   5 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_m_type,type,
    v_m: $i ).

thf(c_Zorn_OTFin_type,type,
    c_Zorn_OTFin: $i > $i > $i ).

thf(v_S_type,type,
    v_S: $i ).

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

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

thf(v_n_type,type,
    v_n: $i ).

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

thf(c_Zorn_Osucc_type,type,
    c_Zorn_Osucc: $i > $i > $i > $i ).

thf(c_Zorn_OTFin__linear__lemma1__1_type,type,
    c_Zorn_OTFin__linear__lemma1__1: $i > $i > $i > $i ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C )
       != A )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).

thf(25,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C )
       != A )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(3,negated_conjecture,
    ~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(14,plain,
    ~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( tc_set @ ( tc_set @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).

thf(20,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( tc_set @ ( tc_set @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(2,negated_conjecture,
    c_in @ v_n @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(13,plain,
    c_in @ v_n @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1,negated_conjecture,
    c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(12,plain,
    c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(5,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).

thf(18,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)],[5]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).

thf(23,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).

thf(30,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(4,negated_conjecture,
    ~ ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(15,plain,
    ~ ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_lessequals @ ( c_Zorn_Osucc @ B @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).

thf(28,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_lessequals @ ( c_Zorn_Osucc @ B @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( 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_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).

thf(21,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
      | ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(33,plain,
    $false,
    inference(e,[status(thm)],[25,14,20,13,12,18,23,30,15,28,21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SET858-2 : TPTP v8.2.0. Released v3.2.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 300
% 0.10/0.29  % DateTime : Mon May 20 13:00:53 EDT 2024
% 0.10/0.29  % CPUTime  : 
% 0.67/0.69  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.94/0.80  % [INFO] 	 Parsing done (105ms). 
% 0.94/0.81  % [INFO] 	 Running in sequential loop mode. 
% 1.30/1.03  % [INFO] 	 eprover registered as external prover. 
% 1.30/1.03  % [INFO] 	 cvc4 registered as external prover. 
% 1.30/1.03  % [INFO] 	 Scanning for conjecture ... 
% 1.56/1.09  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 1.56/1.11  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.56/1.13  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.56/1.14  % [INFO] 	 Type checking passed. 
% 1.56/1.14  % [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 ... 
% 2.53/1.50  % External prover 'e' found a proof!
% 2.53/1.50  % [INFO] 	 Killing All external provers ... 
% 2.53/1.50  % Time passed: 1097ms (effective reasoning time: 684ms)
% 2.53/1.50  % Axioms used in derivation (7): cls_Zorn_OTFin__linear__lemma1_0, cls_Zorn_OTFin__linear__lemma1_3, cls_Set_Osubset__trans_0, cls_Zorn_OTFin__linear__lemma1_2, cls_Zorn_OAbrial__axiom1_0, cls_Zorn_OTFin__linear__lemma2_0, cls_Zorn_OTFin__linear__lemma1_1
% 2.53/1.50  % No. of inferences in proof: 23
% 2.53/1.50  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1097 ms resp. 684 ms w/o parsing
% 2.75/1.57  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.75/1.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------