TSTP Solution File: LAT005-10 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT005-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 11:26:38 EDT 2023

% Result   : Unsatisfiable 69.73s 12.28s
% Output   : Refutation 69.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  117 (  70 unt;  13 typ;   0 def)
%            Number of atoms       :  167 ( 166 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  632 (  95   ~;  63   |;   0   &; 474   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   8 con; 0-4 aty)
%            Number of variables   :  138 (   0   ^; 138   !;   0   ?; 138   :)

% Comments : 
%------------------------------------------------------------------------------
thf(r1_type,type,
    r1: $i ).

thf(meet_type,type,
    meet: $i > $i > $i ).

thf(join_type,type,
    join: $i > $i > $i ).

thf(r2_type,type,
    r2: $i ).

thf(b_type,type,
    b: $i ).

thf(a_type,type,
    a: $i ).

thf(ifeq_type,type,
    ifeq: $i > $i > $i > $i > $i ).

thf(ifeq2_type,type,
    ifeq2: $i > $i > $i > $i > $i ).

thf(ifeq3_type,type,
    ifeq3: $i > $i > $i > $i > $i ).

thf(n1_type,type,
    n1: $i ).

thf(n0_type,type,
    n0: $i ).

thf(complement_type,type,
    complement: $i > $i > $i ).

thf(true_type,type,
    true: $i ).

thf(17,axiom,
    ! [A: $i] :
      ( ( join @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).

thf(56,plain,
    ! [A: $i] :
      ( ( join @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq3 @ ( meet @ A @ B ) @ A @ ( meet @ B @ ( join @ A @ C ) ) @ ( join @ A @ ( meet @ C @ B ) ) )
      = ( join @ A @ ( meet @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).

thf(52,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq3 @ ( meet @ A @ B ) @ A @ ( meet @ B @ ( join @ A @ C ) ) @ ( join @ A @ ( meet @ C @ B ) ) )
      = ( join @ A @ ( meet @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( join @ A @ n0 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).

thf(60,plain,
    ! [A: $i] :
      ( ( join @ A @ n0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(61,plain,
    ! [A: $i] :
      ( ( join @ A @ n0 )
      = A ),
    inference(lifteq,[status(thm)],[60]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( join @ A @ B )
      = ( join @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).

thf(40,plain,
    ! [B: $i,A: $i] :
      ( ( join @ A @ B )
      = ( join @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(41,plain,
    ! [B: $i,A: $i] :
      ( ( join @ A @ B )
      = ( join @ B @ A ) ),
    inference(lifteq,[status(thm)],[40]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( join @ A @ n1 )
      = n1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).

thf(38,plain,
    ! [A: $i] :
      ( ( join @ A @ n1 )
      = n1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(39,plain,
    ! [A: $i] :
      ( ( join @ A @ n1 )
      = n1 ),
    inference(lifteq,[status(thm)],[38]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ( join @ A @ ( meet @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).

thf(34,plain,
    ! [B: $i,A: $i] :
      ( ( join @ A @ ( meet @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(35,plain,
    ! [B: $i,A: $i] :
      ( ( join @ A @ ( meet @ A @ B ) )
      = A ),
    inference(lifteq,[status(thm)],[34]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( join @ A @ B ) @ n1 @ ( ifeq2 @ ( meet @ A @ B ) @ n0 @ ( complement @ A @ B ) @ true ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( join @ A @ B ) @ n1 @ ( ifeq2 @ ( meet @ A @ B ) @ n0 @ ( complement @ A @ B ) @ true ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(43,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( join @ A @ B ) @ n1 @ ( ifeq2 @ ( meet @ A @ B ) @ n0 @ ( complement @ A @ B ) @ true ) @ true )
      = true ),
    inference(lifteq,[status(thm)],[42]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( meet @ A @ n0 )
      = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).

thf(48,plain,
    ! [A: $i] :
      ( ( meet @ A @ n0 )
      = n0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(49,plain,
    ! [A: $i] :
      ( ( meet @ A @ n0 )
      = n0 ),
    inference(lifteq,[status(thm)],[48]) ).

thf(1,negated_conjecture,
    ( r1
   != ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).

thf(23,plain,
    ( r1
   != ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(24,plain,
    ( r1
   != ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
    inference(polarity_switch,[status(thm)],[23]) ).

thf(25,plain,
    ( ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) )
   != r1 ),
    inference(lifteq,[status(thm)],[24]) ).

thf(77,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( ( meet @ A @ n0 )
       != ( meet @ ( join @ r1 @ ( meet @ r2 @ b ) ) @ ( join @ r1 @ ( meet @ r2 @ a ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[49,25]) ).

thf(82,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( A
       != ( join @ r1 @ ( meet @ r2 @ b ) ) )
      | ( ( join @ r1 @ ( meet @ r2 @ a ) )
       != n0 ) ),
    inference(simp,[status(thm)],[77]) ).

thf(87,plain,
    ( ( n0 != r1 )
    | ( ( join @ r1 @ ( meet @ r2 @ a ) )
     != n0 ) ),
    inference(simp,[status(thm)],[82]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ B )
      = ( meet @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).

thf(58,plain,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ B )
      = ( meet @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(91,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( ( join @ r1 @ n0 )
       != n0 )
      | ( ( meet @ A @ n0 )
       != ( meet @ r2 @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[49,87]) ).

thf(93,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( ( join @ r1 @ n0 )
       != n0 )
      | ( A != r2 )
      | ( n0 != a ) ),
    inference(simp,[status(thm)],[91]) ).

thf(95,plain,
    ( ( n0 != r1 )
    | ( ( join @ r1 @ n0 )
     != n0 )
    | ( n0 != a ) ),
    inference(simp,[status(thm)],[93]) ).

thf(121,plain,
    ( ( n0 != r1 )
    | ( n0 != r1 )
    | ( n0 != a ) ),
    inference(rewrite,[status(thm)],[95,61]) ).

thf(122,plain,
    ( ( n0 != r1 )
    | ( n0 != a ) ),
    inference(simp,[status(thm)],[121]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( meet @ A @ n1 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).

thf(36,plain,
    ! [A: $i] :
      ( ( meet @ A @ n1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(37,plain,
    ! [A: $i] :
      ( ( meet @ A @ n1 )
      = A ),
    inference(lifteq,[status(thm)],[36]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( complement @ A @ B ) @ true @ ( join @ A @ B ) @ n1 )
      = n1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).

thf(46,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( complement @ A @ B ) @ true @ ( join @ A @ B ) @ n1 )
      = n1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(57,plain,
    ! [A: $i] :
      ( ( join @ A @ A )
      = A ),
    inference(lifteq,[status(thm)],[56]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).

thf(28,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    inference(lifteq,[status(thm)],[28]) ).

thf(100,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( ( join @ r1 @ A )
       != n0 )
      | ( ( meet @ A @ n1 )
       != ( meet @ r2 @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[37,87]) ).

thf(111,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( ( join @ r1 @ A )
       != n0 )
      | ( A != r2 )
      | ( n1 != a ) ),
    inference(simp,[status(thm)],[100]) ).

thf(117,plain,
    ( ( n0 != r1 )
    | ( ( join @ r1 @ r2 )
     != n0 )
    | ( n1 != a ) ),
    inference(simp,[status(thm)],[111]) ).

thf(14,axiom,
    ( ( complement @ r1 @ ( join @ a @ b ) )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).

thf(50,plain,
    ( ( complement @ r1 @ ( join @ a @ b ) )
    = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(51,plain,
    ( ( complement @ r1 @ ( join @ a @ b ) )
    = true ),
    inference(lifteq,[status(thm)],[50]) ).

thf(259,plain,
    ! [B: $i,A: $i] :
      ( ( ( complement @ r1 @ ( join @ B @ A ) )
        = true )
      | ( ( join @ A @ B )
       != ( join @ a @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[41,51]) ).

thf(260,plain,
    ( ( complement @ r1 @ ( join @ b @ a ) )
    = true ),
    inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).

thf(59,plain,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ B )
      = ( meet @ B @ A ) ),
    inference(lifteq,[status(thm)],[58]) ).

thf(20,axiom,
    ( ( complement @ r2 @ ( meet @ a @ b ) )
    = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).

thf(62,plain,
    ( ( complement @ r2 @ ( meet @ a @ b ) )
    = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(63,plain,
    ( ( complement @ r2 @ ( meet @ a @ b ) )
    = true ),
    inference(lifteq,[status(thm)],[62]) ).

thf(629,plain,
    ! [B: $i,A: $i] :
      ( ( ( complement @ r2 @ ( meet @ B @ A ) )
        = true )
      | ( ( meet @ A @ B )
       != ( meet @ a @ b ) ) ),
    inference(paramod_ordered,[status(thm)],[59,63]) ).

thf(630,plain,
    ( ( complement @ r2 @ ( meet @ b @ a ) )
    = true ),
    inference(pattern_uni,[status(thm)],[629:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( meet @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).

thf(32,plain,
    ! [A: $i] :
      ( ( meet @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(33,plain,
    ! [A: $i] :
      ( ( meet @ A @ A )
      = A ),
    inference(lifteq,[status(thm)],[32]) ).

thf(641,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( meet @ B @ A )
        = C )
      | ( ( meet @ A @ B )
       != ( meet @ C @ n1 ) ) ),
    inference(paramod_ordered,[status(thm)],[59,37]) ).

thf(642,plain,
    ! [A: $i] :
      ( ( meet @ n1 @ A )
      = A ),
    inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( A )),bind(B,$thf( n1 )),bind(C,$thf( A ))]]) ).

thf(92,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( n0 != n1 )
      | ( ( join @ A @ n1 )
       != ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[39,87]) ).

thf(94,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( n0 != n1 )
      | ( A != r1 )
      | ( ( meet @ r2 @ a )
       != n1 ) ),
    inference(simp,[status(thm)],[92]) ).

thf(96,plain,
    ( ( n0 != r1 )
    | ( n0 != n1 )
    | ( ( meet @ r2 @ a )
     != n1 ) ),
    inference(simp,[status(thm)],[94]) ).

thf(243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( join @ B @ A )
        = n1 )
      | ( ( join @ A @ B )
       != ( join @ C @ n1 ) ) ),
    inference(paramod_ordered,[status(thm)],[41,39]) ).

thf(244,plain,
    ! [A: $i] :
      ( ( join @ n1 @ A )
      = n1 ),
    inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( A )),bind(B,$thf( n1 )),bind(C,$thf( A ))]]) ).

thf(329,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( n0 != n1 )
      | ( ( join @ n1 @ A )
       != ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[244,87]) ).

thf(338,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( n0 != n1 )
      | ( n1 != r1 )
      | ( A
       != ( meet @ r2 @ a ) ) ),
    inference(simp,[status(thm)],[329]) ).

thf(343,plain,
    ( ( n0 != r1 )
    | ( n0 != n1 )
    | ( n1 != r1 ) ),
    inference(simp,[status(thm)],[338]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ ( join @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ ( join @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(45,plain,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ ( join @ A @ B ) )
      = A ),
    inference(lifteq,[status(thm)],[44]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( complement @ A @ B ) @ true @ ( meet @ A @ B ) @ n0 )
      = n0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).

thf(64,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( complement @ A @ B ) @ true @ ( meet @ A @ B ) @ n0 )
      = n0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(235,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( join @ B @ A )
        = C )
      | ( ( join @ A @ B )
       != ( join @ C @ n0 ) ) ),
    inference(paramod_ordered,[status(thm)],[41,61]) ).

thf(236,plain,
    ! [A: $i] :
      ( ( join @ n0 @ A )
      = A ),
    inference(pattern_uni,[status(thm)],[235:[bind(A,$thf( A )),bind(B,$thf( n0 )),bind(C,$thf( A ))]]) ).

thf(371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( join @ n0 @ A )
       != ( join @ B @ ( meet @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[236,35]) ).

thf(372,plain,
    ! [A: $i] :
      ( ( meet @ n0 @ A )
      = n0 ),
    inference(pattern_uni,[status(thm)],[371:[bind(A,$thf( meet @ n0 @ E )),bind(B,$thf( n0 )),bind(C,$thf( E ))]]) ).

thf(402,plain,
    ! [A: $i] :
      ( ( meet @ n0 @ A )
      = n0 ),
    inference(simp,[status(thm)],[372]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( join @ ( join @ A @ B ) @ C )
      = ( join @ A @ ( join @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).

thf(54,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( join @ ( join @ A @ B ) @ C )
      = ( join @ A @ ( join @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(125,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( A != n0 )
      | ( ( join @ A @ n0 )
       != ( join @ r1 @ ( meet @ r2 @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[61,87]) ).

thf(130,plain,
    ( ( n0 != r1 )
    | ( n0 != r1 )
    | ( ( meet @ r2 @ a )
     != n0 ) ),
    inference(simp,[status(thm)],[125]) ).

thf(136,plain,
    ( ( n0 != r1 )
    | ( ( meet @ r2 @ a )
     != n0 ) ),
    inference(simp,[status(thm)],[130]) ).

thf(459,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( ( meet @ n0 @ A )
       != ( meet @ r2 @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[402,136]) ).

thf(481,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( n0 != r2 )
      | ( A != a ) ),
    inference(simp,[status(thm)],[459]) ).

thf(483,plain,
    ( ( n0 != r1 )
    | ( n0 != r2 ) ),
    inference(simp,[status(thm)],[481]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( meet @ ( meet @ A @ B ) @ C )
      = ( meet @ A @ ( meet @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).

thf(66,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( meet @ ( meet @ A @ B ) @ C )
      = ( meet @ A @ ( meet @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq3 @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq3 @ A @ A @ B @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(31,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq3 @ A @ A @ B @ C )
      = B ),
    inference(lifteq,[status(thm)],[30]) ).

thf(301,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( n0 != n1 )
      | ( A != n1 )
      | ( ( meet @ A @ n1 )
       != ( meet @ r2 @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[37,96]) ).

thf(305,plain,
    ( ( n0 != r1 )
    | ( n0 != n1 )
    | ( n1 != r2 )
    | ( n1 != a ) ),
    inference(simp,[status(thm)],[301]) ).

thf(147,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( ( join @ r1 @ A )
       != n0 )
      | ( ( meet @ A @ A )
       != ( meet @ r2 @ a ) ) ),
    inference(paramod_ordered,[status(thm)],[33,87]) ).

thf(158,plain,
    ! [A: $i] :
      ( ( n0 != r1 )
      | ( ( join @ r1 @ A )
       != n0 )
      | ( A != r2 )
      | ( A != a ) ),
    inference(simp,[status(thm)],[147]) ).

thf(163,plain,
    ( ( n0 != r1 )
    | ( ( join @ r1 @ r2 )
     != n0 )
    | ( a != r2 ) ),
    inference(simp,[status(thm)],[158]) ).

thf(41316,plain,
    $false,
    inference(cvc4,[status(thm)],[56,52,61,41,39,35,43,87,58,122,42,37,25,46,57,29,60,117,260,630,33,28,38,642,96,343,244,45,64,32,34,402,44,59,27,54,49,236,483,66,48,63,50,31,40,26,23,36,30,51,305,136,163,62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT005-10 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n028.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu May 18 14:18:19 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 1.07/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.31/1.06  % [INFO] 	 Parsing done (136ms). 
% 1.31/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.92/1.33  % [INFO] 	 Found a conjecture and 21 axioms. Running axiom selection ... 
% 2.08/1.37  % [INFO] 	 Axiom selection finished. Selected 21 axioms (removed 0 axioms). 
% 2.08/1.39  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.08/1.40  % [INFO] 	 Type checking passed. 
% 2.08/1.40  % [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 ... 
% 69.73/12.28  % External prover 'cvc4' found a proof!
% 69.73/12.28  % [INFO] 	 Killing All external provers ... 
% 69.73/12.28  % Time passed: 11756ms (effective reasoning time: 11206ms)
% 69.73/12.28  % 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)>
% 69.73/12.28  % Axioms used in derivation (21): ifeq_axiom_001, meet_join_complement, commutativity_of_meet, x_join_0, x_meet_1, associativity_of_join, idempotence_of_meet, x_meet_0, complement_of_a_meet_b, ifeq_axiom_002, ifeq_axiom, commutativity_of_join, absorption1, x_join_1, modular, associativity_of_meet, complement_join, complement_meet, complement_of_a_join_b, idempotence_of_join, absorption2
% 69.73/12.28  % No. of inferences in proof: 104
% 69.73/12.28  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11756 ms resp. 11206 ms w/o parsing
% 69.73/12.31  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 69.73/12.31  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------