TSTP Solution File: LAT268-2 by Leo-III-SAT---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : LAT268-2 : 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 : Tue May  7 10:39:07 EDT 2024

% Result   : Unsatisfiable 13.90s 3.32s
% Output   : Refutation 13.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   63 (  28 unt;  20 typ;   0 def)
%            Number of atoms       :   84 (  16 equ;   0 cnn)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  718 (  37   ~;  33   |;   0   &; 648   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  20 usr;  11 con; 0-4 aty)
%            Number of variables   :   55 (   0   ^  55   !;   0   ?;  55   :)

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

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

thf(c_Tarski_Oglb_type,type,
    c_Tarski_Oglb: $i > $i > $i > $i ).

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

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

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

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

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

thf(c_Tarski_OCompleteLattice_type,type,
    c_Tarski_OCompleteLattice: $i ).

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

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

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

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

thf(c_Tarski_Odual_type,type,
    c_Tarski_Odual: $i > $i > $i ).

thf(3,negated_conjecture,
    ~ ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(14,plain,
    ~ ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_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(15,plain,
    ~ ( c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
    inference(polarity_switch,[status(thm)],[14]) ).

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

thf(12,plain,
    c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2,negated_conjecture,
    c_in @ v_x @ v_S @ t_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

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

thf(7,axiom,
    c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).

thf(22,plain,
    c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ D @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
      | ~ ( c_in @ D @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_set @ C ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ D @ C ) @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).

thf(18,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ D @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
      | ~ ( c_in @ D @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_set @ C ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ D @ C ) @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(19,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ D @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
      | ~ ( c_in @ D @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_set @ C ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ D @ C ) @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
    inference(cnf,[status(esa)],[18]) ).

thf(46,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ D @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_set @ C ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ D @ C ) @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) )
      | ( ( c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
       != ( c_in @ D @ c_Tarski_OCompleteLattice @ ( tc_Tarski_Opotype_Opotype__ext__type @ C @ tc_Product__Type_Ounit ) ) ) ),
    inference(paramod_ordered,[status(thm)],[22,19]) ).

thf(47,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ t_a )
      | ~ ( c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Olub @ B @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_a )),bind(D,$thf( c_Tarski_Odual @ v_cl @ t_a ))]]) ).

thf(8,axiom,
    c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).

thf(23,plain,
    c_in @ ( c_Tarski_Odual @ v_cl @ t_a ) @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Oglb @ A @ B @ C )
      = ( c_Tarski_Olub @ A @ ( c_Tarski_Odual @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Oglb @ A @ B @ C )
      = ( c_Tarski_Olub @ A @ ( c_Tarski_Odual @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Tarski_Olub @ A @ ( c_Tarski_Odual @ B @ C ) @ C )
      = ( c_Tarski_Oglb @ A @ B @ C ) ),
    inference(lifteq,[status(thm)],[24]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ A @ B ) @ B @ tc_Product__Type_Ounit )
      = ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ A @ B ) @ B @ tc_Product__Type_Ounit )
      = ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ( c_Tarski_Opotype_Opset @ ( c_Tarski_Odual @ A @ B ) @ B @ tc_Product__Type_Ounit )
      = ( c_Tarski_Opotype_Opset @ A @ B @ tc_Product__Type_Ounit ) ),
    inference(lifteq,[status(thm)],[26]) ).

thf(874,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ t_a )
      | ~ $true
      | ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Oglb @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(rewrite,[status(thm)],[47,23,25,27]) ).

thf(875,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ t_a )
      | ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Oglb @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(simp,[status(thm)],[874]) ).

thf(885,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ B @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ A @ ( c_Tarski_Oglb @ B @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ( ( c_in @ v_x @ v_S @ t_a )
       != ( c_in @ A @ B @ t_a ) ) ),
    inference(paramod_ordered,[status(thm)],[13,875]) ).

thf(886,plain,
    ( ~ ( c_lessequals @ v_S @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_set @ t_a ) )
    | ( c_in @ ( c_Pair @ v_x @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(pattern_uni,[status(thm)],[885:[bind(A,$thf( v_x )),bind(B,$thf( v_S ))]]) ).

thf(4,axiom,
    ( v_A
    = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).

thf(16,plain,
    ( v_A
    = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(17,plain,
    ( ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit )
    = v_A ),
    inference(lifteq,[status(thm)],[16]) ).

thf(1009,plain,
    ( ~ ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
    | ( c_in @ ( c_Pair @ v_x @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    inference(rewrite,[status(thm)],[886,17]) ).

thf(1027,plain,
    ( ( c_in @ ( c_Pair @ v_x @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
    | ( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
     != ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,1009]) ).

thf(1028,plain,
    c_in @ ( c_Pair @ v_x @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ),
    inference(pattern_uni,[status(thm)],[1027:[]]) ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ D @ C ) @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).

thf(20,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ D @ C ) @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(21,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ D @ C ) @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) )
      | ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ),
    inference(cnf,[status(esa)],[20]) ).

thf(1103,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ D @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) )
      | ( ( c_in @ ( c_Pair @ v_x @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ v_cl @ t_a ) @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
       != ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Tarski_Opotype_Oorder @ ( c_Tarski_Odual @ D @ C ) @ C @ tc_Product__Type_Ounit ) @ ( tc_prod @ C @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1028,21]) ).

thf(1104,plain,
    c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ),
    inference(pattern_uni,[status(thm)],[1103:[bind(A,$thf( v_x )),bind(B,$thf( c_Tarski_Oglb @ v_S @ v_cl @ t_a )),bind(C,$thf( t_a )),bind(D,$thf( v_cl ))]]) ).

thf(11,axiom,
    ( v_r
    = ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).

thf(28,plain,
    ( v_r
    = ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(29,plain,
    ( ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit )
    = v_r ),
    inference(lifteq,[status(thm)],[28]) ).

thf(1172,plain,
    c_in @ ( c_Pair @ ( c_Tarski_Oglb @ v_S @ v_cl @ t_a ) @ v_x @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
    inference(rewrite,[status(thm)],[1104,29]) ).

thf(1173,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[15,1172]) ).

thf(1174,plain,
    $false,
    inference(simp,[status(thm)],[1173]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT268-2 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.15  % 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 : Mon May  6 18:08:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.95/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.27/0.96  % [INFO] 	 Parsing done (116ms). 
% 1.27/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.17  % [INFO] 	 nitpick registered as external prover. 
% 1.69/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.23  % [INFO] 	 Found a conjecture and 8 axioms. Running axiom selection ... 
% 1.90/1.25  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.90/1.27  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.90/1.27  % [INFO] 	 Type checking passed. 
% 1.90/1.27  % [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 ... 
% 13.63/3.31  % [INFO] 	 Killing All external provers ... 
% 13.90/3.32  % Time passed: 2803ms (effective reasoning time: 2349ms)
% 13.90/3.32  % 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)>
% 13.90/3.32  % Axioms used in derivation (8): cls_Tarski_OCL_Olub__upper_0, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Tarski_Oglb__dual__lub_0, cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0, cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0, cls_Tarski_Odual_Acl_A_58_APartialOrder_0, cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0
% 13.90/3.32  % No. of inferences in proof: 43
% 13.90/3.32  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2803 ms resp. 2349 ms w/o parsing
% 13.90/3.35  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.90/3.35  % [INFO] 	 Killing All external provers ... 
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