TSTP Solution File: LAT281-2 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LAT281-2 : 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 : Mon May 20 23:30:41 EDT 2024

% Result   : Unsatisfiable 4.76s 2.45s
% Output   : Refutation 4.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   44 (  17 unt;  14 typ;   0 def)
%            Number of atoms       :   60 (   6 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  430 (  35   ~;  24   |;   0   &; 371   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;  10 con; 0-4 aty)
%            Number of variables   :   33 (   0   ^  33   !;   0   ?;  33   :)

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

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

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

thf(v_c_type,type,
    v_c: $i ).

thf(c_Relation_Otrans_type,type,
    c_Relation_Otrans: $i > $i > $o ).

thf(c_Tarski_OPartialOrder_type,type,
    c_Tarski_OPartialOrder: $i ).

thf(tc_Tarski_Opotype_Opotype__ext__type_type,type,
    tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).

thf(tc_Product__Type_Ounit_type,type,
    tc_Product__Type_Ounit: $i ).

thf(c_Tarski_Opotype_Oorder_type,type,
    c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).

thf(v_cl_type,type,
    v_cl: $i ).

thf(2,negated_conjecture,
    c_in @ ( c_Pair @ v_b @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(9,plain,
    c_in @ ( c_Pair @ v_b @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Relation_Otrans @ A @ B )
      | ~ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
      | ~ ( c_in @ ( c_Pair @ E @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
      | ( c_in @ ( c_Pair @ E @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Otrans__def_0) ).

thf(12,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Relation_Otrans @ A @ B )
      | ~ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
      | ~ ( c_in @ ( c_Pair @ E @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
      | ( c_in @ ( c_Pair @ E @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Relation_Otrans @ A @ B )
      | ~ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
      | ~ ( c_in @ ( c_Pair @ E @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
      | ( c_in @ ( c_Pair @ E @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(3,negated_conjecture,
    ~ ( c_in @ ( c_Pair @ v_a @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(10,plain,
    ~ ( c_in @ ( c_Pair @ v_a @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,plain,
    ~ ( c_in @ ( c_Pair @ v_a @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(51,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Relation_Otrans @ A @ B )
      | ~ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
      | ~ ( c_in @ ( c_Pair @ E @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
      | ( ( c_in @ ( c_Pair @ E @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
       != ( c_in @ ( c_Pair @ v_a @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13,11]) ).

thf(52,plain,
    ! [A: $i] :
      ( ~ ( c_Relation_Otrans @ v_r @ t_a )
      | ~ ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( v_r )),bind(B,$thf( t_a )),bind(C,$thf( C )),bind(D,$thf( v_c )),bind(E,$thf( v_a ))]]) ).

thf(70,plain,
    ! [A: $i] :
      ( ~ ( c_Relation_Otrans @ v_r @ t_a )
      | ~ ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(simp,[status(thm)],[52]) ).

thf(6,axiom,
    c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).

thf(16,plain,
    c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_2) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
      | ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B )
      | ( ( c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
       != ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) ) ) ),
    inference(paramod_ordered,[status(thm)],[16,15]) ).

thf(33,plain,
    c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a,
    inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( v_cl )),bind(B,$thf( t_a ))]]) ).

thf(7,axiom,
    ( v_r
    = ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).

thf(17,plain,
    ( v_r
    = ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(18,plain,
    ( ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit )
    = v_r ),
    inference(lifteq,[status(thm)],[17]) ).

thf(77,plain,
    c_Relation_Otrans @ v_r @ t_a,
    inference(rewrite,[status(thm)],[33,18]) ).

thf(83,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(rewrite,[status(thm)],[70,77]) ).

thf(84,plain,
    ! [A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(simp,[status(thm)],[83]) ).

thf(85,plain,
    ! [A: $i] :
      ( ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ( ( c_in @ ( c_Pair @ v_b @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
       != ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9,84]) ).

thf(86,plain,
    ~ ( c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( v_b ))]]) ).

thf(1,negated_conjecture,
    c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(8,plain,
    c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(109,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[86,8]) ).

thf(110,plain,
    $false,
    inference(simp,[status(thm)],[109]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : LAT281-2 : TPTP v8.2.0. Released v3.2.0.
% 0.10/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n006.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sun May 19 19:54:54 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.93/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/1.05  % [INFO] 	 Parsing done (155ms). 
% 1.18/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.42  % [INFO] 	 nitpick registered as external prover. 
% 1.74/1.42  % [INFO] 	 Scanning for conjecture ... 
% 1.94/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 1.99/1.54  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.99/1.56  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.99/1.56  % [INFO] 	 Type checking passed. 
% 1.99/1.56  % [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 ... 
% 4.76/2.44  % [INFO] 	 Killing All external provers ... 
% 4.76/2.45  % Time passed: 1994ms (effective reasoning time: 1372ms)
% 4.76/2.45  % Axioms used in derivation (4): cls_Relation_Otrans__def_0, cls_Tarski_Ocl_A_58_APartialOrder_0, cls_Tarski_OPartialOrder__iff_2, cls_Tarski_Or_A_61_61_Aorder_Acl_0
% 4.76/2.45  % No. of inferences in proof: 30
% 4.76/2.45  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1994 ms resp. 1372 ms w/o parsing
% 4.76/2.50  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.76/2.51  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------