TSTP Solution File: LAT271-2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LAT271-2 : 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 : Mon May 20 23:30:38 EDT 2024

% Result   : Unsatisfiable 4.26s 2.30s
% Output   : Refutation 4.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   29 (  10 unt;  12 typ;   0 def)
%            Number of atoms       :   32 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  213 (  20   ~;  11   |;   0   &; 182   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   8 con; 0-4 aty)
%            Number of variables   :   30 (   0   ^  30   !;   0   ?;  30   :)

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

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

thf(c_Tarski_Ointerval_type,type,
    c_Tarski_Ointerval: $i > $i > $i > $i > $i ).

thf(v_r_type,type,
    v_r: $i ).

thf(v_a_type,type,
    v_a: $i ).

thf(v_b_type,type,
    v_b: $i ).

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

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

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

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

thf(c_Pair_type,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(tc_prod_type,type,
    tc_prod: $i > $i > $i ).

thf(1,negated_conjecture,
    c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(5,plain,
    c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(4,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Ointerval @ D @ E @ F @ C ) @ ( tc_set @ C ) )
      | ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0) ).

thf(9,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Ointerval @ D @ E @ F @ C ) @ ( tc_set @ C ) )
      | ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Ointerval @ D @ E @ F @ C ) @ ( tc_set @ C ) )
      | ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(3,negated_conjecture,
    ~ ( c_in @ ( c_Pair @ v_a @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).

thf(7,plain,
    ~ ( c_in @ ( c_Pair @ v_a @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,plain,
    ~ ( c_in @ ( c_Pair @ v_a @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(19,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Ointerval @ D @ E @ F @ C ) @ ( tc_set @ C ) )
      | ( ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
       != ( c_in @ ( c_Pair @ v_a @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,8]) ).

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ v_x @ A @ t_a )
      | ~ ( c_lessequals @ A @ ( c_Tarski_Ointerval @ v_r @ v_a @ B @ t_a ) @ ( tc_set @ t_a ) ) ),
    inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( v_x )),bind(B,$thf( B )),bind(C,$thf( t_a )),bind(D,$thf( v_r )),bind(E,$thf( v_a ))]]) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ v_x @ A @ t_a )
      | ~ ( c_lessequals @ A @ ( c_Tarski_Ointerval @ v_r @ v_a @ B @ t_a ) @ ( tc_set @ t_a ) ) ),
    inference(simp,[status(thm)],[20]) ).

thf(24,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ v_x @ A @ t_a )
      | ( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) )
       != ( c_lessequals @ A @ ( c_Tarski_Ointerval @ v_r @ v_a @ B @ t_a ) @ ( tc_set @ t_a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5,23]) ).

thf(25,plain,
    ~ ( c_in @ v_x @ v_S @ t_a ),
    inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( v_S )),bind(B,$thf( v_b ))]]) ).

thf(2,negated_conjecture,
    c_in @ v_x @ v_S @ t_a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(6,plain,
    c_in @ v_x @ v_S @ t_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(48,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[25,6]) ).

thf(49,plain,
    $false,
    inference(simp,[status(thm)],[48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : LAT271-2 : TPTP v8.2.0. Released v3.2.0.
% 0.11/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n032.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun May 19 20:24:23 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.00/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.29/1.09  % [INFO] 	 Parsing done (149ms). 
% 1.29/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.85/1.46  % [INFO] 	 nitpick registered as external prover. 
% 1.85/1.47  % [INFO] 	 Scanning for conjecture ... 
% 2.01/1.56  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 2.01/1.59  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 2.01/1.60  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.01/1.60  % [INFO] 	 Type checking passed. 
% 2.12/1.60  % [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 ... 
% 3.39/2.29  % [INFO] 	 Killing All external provers ... 
% 3.39/2.29  % Time passed: 1809ms (effective reasoning time: 1181ms)
% 3.39/2.30  % Axioms used in derivation (1): cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0
% 3.39/2.30  % No. of inferences in proof: 17
% 4.26/2.30  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1809 ms resp. 1181 ms w/o parsing
% 4.26/2.34  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.26/2.34  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------