TSTP Solution File: LAT276-2 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT276-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 11:27:17 EDT 2023

% Result   : Unsatisfiable 3.26s 1.81s
% Output   : Refutation 3.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   41 (   7 unt;  16 typ;   0 def)
%            Number of atoms       :   59 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  464 (  30   ~;  34   |;   0   &; 400   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   8 con; 0-4 aty)
%            Number of variables   :   24 (   0   ^;  24   !;   0   ?;  24   :)

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

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

thf(v_A_type,type,
    v_A: $i ).

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

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

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_xa_type,type,
    v_xa: $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(tc_Product__Type_Ounit_type,type,
    tc_Product__Type_Ounit: $i ).

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

thf(c_Tarski_Olub_type,type,
    c_Tarski_Olub: $i > $i > $i > $i ).

thf(c_Tarski_Opotype_Opset_type,type,
    c_Tarski_Opotype_Opset: $i > $i > $i > $i ).

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

thf(v_sko__4mP_type,type,
    v_sko__4mP: $i > $i > $i > $i ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(24,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

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

thf(14,plain,
    c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ v_A @ t_a )
      | ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ( c_in @ ( v_sko__4mP @ A @ B @ v_r ) @ B @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ v_A @ t_a )
      | ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ( c_in @ ( v_sko__4mP @ A @ B @ v_r ) @ B @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(5,negated_conjecture,
    ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
    | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(13,plain,
    ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
    | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(4,negated_conjecture,
    ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
    | ( c_in @ v_xa @ v_S @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(18,plain,
    ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
    | ( c_in @ v_xa @ v_S @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ A @ v_S @ t_a )
      | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_10) ).

thf(16,plain,
    ! [A: $i] :
      ( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ A @ v_S @ t_a )
      | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ( v_A
    = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).

thf(26,plain,
    ( v_A
    = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ v_A @ t_a )
      | ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ A @ B @ v_r ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ v_A @ t_a )
      | ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ A @ B @ v_r ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,negated_conjecture,
    ! [A: $i] :
      ( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ A @ v_S @ t_a )
      | ( c_in @ v_xa @ v_S @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).

thf(15,plain,
    ! [A: $i] :
      ( ( c_in @ ( c_Pair @ A @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ A @ v_S @ t_a )
      | ( c_in @ v_xa @ v_S @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,negated_conjecture,
    ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
    | ( c_in @ v_xa @ v_S @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(17,plain,
    ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
    | ( c_in @ v_xa @ v_S @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ t_a )
      | ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ t_a )
      | ~ ( c_lessequals @ B @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(12,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(34,plain,
    ( v_r
    = ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(36,plain,
    $false,
    inference(e,[status(thm)],[24,14,28,13,18,16,26,30,15,17,32,34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : LAT276-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n003.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 14:19:01 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/0.98  % [INFO] 	 Parsing done (120ms). 
% 1.30/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.80/1.28  % [INFO] 	 cvc4 registered as external prover. 
% 1.80/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.37  % [INFO] 	 Found a conjecture and 6 axioms. Running axiom selection ... 
% 2.06/1.40  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 2.06/1.41  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.06/1.42  % [INFO] 	 Type checking passed. 
% 2.06/1.42  % [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 ... 
% 3.26/1.81  % External prover 'e' found a proof!
% 3.26/1.81  % [INFO] 	 Killing All external provers ... 
% 3.26/1.81  % Time passed: 1304ms (effective reasoning time: 820ms)
% 3.26/1.81  % 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)>
% 3.26/1.81  % Axioms used in derivation (6): cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OsubsetD_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0, cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1
% 3.26/1.81  % No. of inferences in proof: 25
% 3.26/1.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1304 ms resp. 820 ms w/o parsing
% 3.44/1.89  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.44/1.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------