TSTP Solution File: REL009+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : REL009+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 Apr 30 20:37:22 EDT 2024

% Result   : Theorem 201.27s 25.72s
% Output   : CNFRefutation 202.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   44
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  137 ( 121 unt;   0 def)
%            Number of atoms       :  158 ( 142 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   37 (  16   ~;  12   |;   5   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   3 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :  211 ( 204   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X0] : composition(X0,one) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X0] : converse(converse(X0)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X0] : top = join(X0,complement(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X0] : zero = meet(X0,complement(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,conjecture,
    ! [X0,X1,X2] :
      ( join(X0,X1) = X1
     => ( join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2)
        & join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( join(X0,X1) = X1
       => ( join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2)
          & join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1) ) ),
    inference(negated_conjecture,[status(cth)],[f14]) ).

fof(f16,plain,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f17,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f18,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f19,plain,
    ! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f20,plain,
    ! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f21,plain,
    ! [X0] : composition(X0,one) = X0,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f22,plain,
    ! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f23,plain,
    ! [X0] : converse(converse(X0)) = X0,
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f24,plain,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f25,plain,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f26,plain,
    ! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f27,plain,
    ! [X0] : top = join(X0,complement(X0)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f28,plain,
    ! [X0] : zero = meet(X0,complement(X0)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f29,plain,
    ? [X0,X1,X2] :
      ( join(X0,X1) = X1
      & ( join(composition(X0,X2),composition(X1,X2)) != composition(X1,X2)
        | join(composition(X2,X0),composition(X2,X1)) != composition(X2,X1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f30,plain,
    ? [X0,X1] :
      ( join(X0,X1) = X1
      & ( ? [X2] : join(composition(X0,X2),composition(X1,X2)) != composition(X1,X2)
        | ? [X2] : join(composition(X2,X0),composition(X2,X1)) != composition(X2,X1) ) ),
    inference(miniscoping,[status(esa)],[f29]) ).

fof(f31,plain,
    ( join(sk0_0,sk0_1) = sk0_1
    & ( join(composition(sk0_0,sk0_2),composition(sk0_1,sk0_2)) != composition(sk0_1,sk0_2)
      | join(composition(sk0_3,sk0_0),composition(sk0_3,sk0_1)) != composition(sk0_3,sk0_1) ) ),
    inference(skolemization,[status(esa)],[f30]) ).

fof(f32,plain,
    join(sk0_0,sk0_1) = sk0_1,
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ( join(composition(sk0_0,sk0_2),composition(sk0_1,sk0_2)) != composition(sk0_1,sk0_2)
    | join(composition(sk0_3,sk0_0),composition(sk0_3,sk0_1)) != composition(sk0_3,sk0_1) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f34,plain,
    ( spl0_0
  <=> join(composition(sk0_0,sk0_2),composition(sk0_1,sk0_2)) = composition(sk0_1,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f36,plain,
    ( join(composition(sk0_0,sk0_2),composition(sk0_1,sk0_2)) != composition(sk0_1,sk0_2)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f34]) ).

fof(f37,plain,
    ( spl0_1
  <=> join(composition(sk0_3,sk0_0),composition(sk0_3,sk0_1)) = composition(sk0_3,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f39,plain,
    ( join(composition(sk0_3,sk0_0),composition(sk0_3,sk0_1)) != composition(sk0_3,sk0_1)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f37]) ).

fof(f40,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f33,f34,f37]) ).

fof(f41,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
    inference(paramodulation,[status(thm)],[f16,f17]) ).

fof(f46,plain,
    ! [X0] : join(sk0_0,join(sk0_1,X0)) = join(sk0_1,X0),
    inference(paramodulation,[status(thm)],[f32,f17]) ).

fof(f47,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),X2),
    inference(paramodulation,[status(thm)],[f16,f17]) ).

fof(f48,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f17,f47]) ).

fof(f115,plain,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X1,X0)),
    inference(paramodulation,[status(thm)],[f16,f41]) ).

fof(f223,plain,
    ( composition(join(sk0_0,sk0_1),sk0_2) != composition(sk0_1,sk0_2)
    | spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f22,f36]) ).

fof(f224,plain,
    ( composition(sk0_1,sk0_2) != composition(sk0_1,sk0_2)
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f32,f223]) ).

fof(f225,plain,
    ( $false
    | spl0_0 ),
    inference(trivial_equality_resolution,[status(esa)],[f224]) ).

fof(f226,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f225]) ).

fof(f249,plain,
    ! [X0,X1] : composition(X0,composition(one,X1)) = composition(X0,X1),
    inference(paramodulation,[status(thm)],[f21,f20]) ).

fof(f250,plain,
    ! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))),
    inference(paramodulation,[status(thm)],[f17,f27]) ).

fof(f251,plain,
    join(sk0_0,top) = join(sk0_1,complement(sk0_1)),
    inference(paramodulation,[status(thm)],[f27,f46]) ).

fof(f252,plain,
    join(top,sk0_0) = join(sk0_1,complement(sk0_1)),
    inference(forward_demodulation,[status(thm)],[f16,f251]) ).

fof(f253,plain,
    join(top,sk0_0) = top,
    inference(forward_demodulation,[status(thm)],[f27,f252]) ).

fof(f260,plain,
    ! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
    inference(paramodulation,[status(thm)],[f27,f17]) ).

fof(f261,plain,
    ! [X0] : meet(X0,complement(X0)) = complement(top),
    inference(paramodulation,[status(thm)],[f27,f19]) ).

fof(f262,plain,
    zero = complement(top),
    inference(forward_demodulation,[status(thm)],[f28,f261]) ).

fof(f263,plain,
    ! [X0,X1] : meet(X0,X1) = complement(join(complement(X1),complement(X0))),
    inference(paramodulation,[status(thm)],[f16,f19]) ).

fof(f264,plain,
    ! [X0,X1] : meet(X0,X1) = meet(X1,X0),
    inference(forward_demodulation,[status(thm)],[f19,f263]) ).

fof(f287,plain,
    ! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
    inference(paramodulation,[status(thm)],[f23,f24]) ).

fof(f346,plain,
    ! [X0,X1] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
    inference(paramodulation,[status(thm)],[f23,f25]) ).

fof(f351,plain,
    ! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
    inference(paramodulation,[status(thm)],[f23,f25]) ).

fof(f353,plain,
    ! [X0,X1,X2] : composition(join(converse(X0),X1),converse(X2)) = join(converse(composition(X2,X0)),composition(X1,converse(X2))),
    inference(paramodulation,[status(thm)],[f25,f22]) ).

fof(f355,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
    inference(forward_demodulation,[status(thm)],[f16,f18]) ).

fof(f356,plain,
    ! [X0,X1] : X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f19,f355]) ).

fof(f357,plain,
    ! [X0,X1] : X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
    inference(forward_demodulation,[status(thm)],[f16,f356]) ).

fof(f362,plain,
    ! [X0,X1] : X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
    inference(paramodulation,[status(thm)],[f19,f357]) ).

fof(f363,plain,
    ! [X0,X1] : X0 = join(meet(X0,X1),meet(X0,complement(X1))),
    inference(forward_demodulation,[status(thm)],[f16,f362]) ).

fof(f371,plain,
    ! [X0,X1] : X0 = join(meet(X0,X1),complement(join(X1,complement(X0)))),
    inference(paramodulation,[status(thm)],[f16,f357]) ).

fof(f382,plain,
    ! [X0,X1] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
    inference(forward_demodulation,[status(thm)],[f16,f26]) ).

fof(f456,plain,
    ! [X0] : join(top,join(X0,sk0_0)) = join(X0,top),
    inference(paramodulation,[status(thm)],[f253,f48]) ).

fof(f620,plain,
    ! [X0,X1] : X0 = join(meet(X1,X0),meet(X0,complement(X1))),
    inference(paramodulation,[status(thm)],[f264,f363]) ).

fof(f624,plain,
    ! [X0,X1] : X0 = join(meet(X0,X1),meet(complement(X1),X0)),
    inference(paramodulation,[status(thm)],[f264,f363]) ).

fof(f626,plain,
    ! [X0] : X0 = join(meet(X0,top),meet(X0,zero)),
    inference(paramodulation,[status(thm)],[f262,f363]) ).

fof(f640,plain,
    ! [X0,X1] : X0 = join(meet(X1,X0),meet(complement(X1),X0)),
    inference(paramodulation,[status(thm)],[f264,f620]) ).

fof(f660,plain,
    ! [X0] : X0 = join(meet(X0,top),meet(zero,X0)),
    inference(paramodulation,[status(thm)],[f262,f624]) ).

fof(f673,plain,
    ! [X0,X1] : join(meet(X0,top),join(X1,meet(X0,zero))) = join(X1,X0),
    inference(paramodulation,[status(thm)],[f626,f48]) ).

fof(f2933,plain,
    ! [X0] : converse(converse(X0)) = composition(converse(one),X0),
    inference(paramodulation,[status(thm)],[f21,f351]) ).

fof(f2934,plain,
    ! [X0] : X0 = composition(converse(one),X0),
    inference(forward_demodulation,[status(thm)],[f23,f2933]) ).

fof(f2961,plain,
    ! [X0] : composition(one,X0) = composition(converse(one),X0),
    inference(paramodulation,[status(thm)],[f249,f2934]) ).

fof(f2962,plain,
    ! [X0] : composition(one,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f2934,f2961]) ).

fof(f3006,plain,
    ! [X0] : join(complement(X0),composition(converse(one),complement(X0))) = complement(X0),
    inference(paramodulation,[status(thm)],[f2962,f382]) ).

fof(f3007,plain,
    ! [X0] : join(complement(X0),complement(X0)) = complement(X0),
    inference(forward_demodulation,[status(thm)],[f2934,f3006]) ).

fof(f3035,plain,
    ! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),complement(X1)))) = complement(join(complement(X0),complement(X1))),
    inference(paramodulation,[status(thm)],[f19,f3007]) ).

fof(f3036,plain,
    ! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = complement(join(complement(X0),complement(X1))),
    inference(forward_demodulation,[status(thm)],[f19,f3035]) ).

fof(f3037,plain,
    ! [X0,X1] : join(meet(X0,X1),meet(X0,X1)) = meet(X0,X1),
    inference(forward_demodulation,[status(thm)],[f19,f3036]) ).

fof(f3046,plain,
    ! [X0] : meet(X0,X0) = complement(complement(X0)),
    inference(paramodulation,[status(thm)],[f3007,f19]) ).

fof(f3168,plain,
    ! [X0] : join(meet(X0,top),meet(X0,zero)) = join(meet(X0,zero),X0),
    inference(paramodulation,[status(thm)],[f3037,f673]) ).

fof(f3169,plain,
    ! [X0] : X0 = join(meet(X0,zero),X0),
    inference(forward_demodulation,[status(thm)],[f626,f3168]) ).

fof(f3170,plain,
    ! [X0] : X0 = join(X0,meet(X0,zero)),
    inference(forward_demodulation,[status(thm)],[f16,f3169]) ).

fof(f3171,plain,
    ! [X0,X1] : top = join(meet(X0,X1),join(meet(X0,X1),complement(meet(X0,X1)))),
    inference(paramodulation,[status(thm)],[f3037,f250]) ).

fof(f3172,plain,
    ! [X0,X1] : top = join(meet(X0,X1),top),
    inference(forward_demodulation,[status(thm)],[f27,f3171]) ).

fof(f3173,plain,
    ! [X0,X1] : top = join(top,meet(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f16,f3172]) ).

fof(f3472,plain,
    ! [X0] : X0 = join(X0,meet(zero,X0)),
    inference(paramodulation,[status(thm)],[f264,f3170]) ).

fof(f3618,plain,
    ! [X0] : join(meet(X0,top),top) = join(top,X0),
    inference(paramodulation,[status(thm)],[f3173,f673]) ).

fof(f3619,plain,
    ! [X0] : join(top,meet(X0,top)) = join(top,X0),
    inference(forward_demodulation,[status(thm)],[f16,f3618]) ).

fof(f3620,plain,
    ! [X0] : top = join(top,X0),
    inference(forward_demodulation,[status(thm)],[f3173,f3619]) ).

fof(f3638,plain,
    ! [X0] : top = join(X0,top),
    inference(backward_demodulation,[status(thm)],[f3620,f456]) ).

fof(f3639,plain,
    ! [X0,X1] : join(X0,join(complement(X0),X1)) = top,
    inference(backward_demodulation,[status(thm)],[f3620,f260]) ).

fof(f3724,plain,
    ! [X0] : X0 = join(meet(X0,top),complement(top)),
    inference(paramodulation,[status(thm)],[f3638,f357]) ).

fof(f3725,plain,
    ! [X0] : X0 = join(complement(top),meet(X0,top)),
    inference(forward_demodulation,[status(thm)],[f16,f3724]) ).

fof(f3726,plain,
    ! [X0] : X0 = join(zero,meet(X0,top)),
    inference(forward_demodulation,[status(thm)],[f262,f3725]) ).

fof(f3951,plain,
    ! [X0,X1] : join(meet(X0,top),join(zero,X1)) = join(X1,X0),
    inference(paramodulation,[status(thm)],[f3726,f115]) ).

fof(f3952,plain,
    ! [X0,X1] : join(zero,join(meet(X0,top),X1)) = join(X1,X0),
    inference(forward_demodulation,[status(thm)],[f48,f3951]) ).

fof(f4159,plain,
    ! [X0] : join(zero,X0) = join(meet(zero,X0),X0),
    inference(paramodulation,[status(thm)],[f660,f3952]) ).

fof(f4160,plain,
    ! [X0] : join(zero,X0) = join(X0,meet(zero,X0)),
    inference(forward_demodulation,[status(thm)],[f16,f4159]) ).

fof(f4161,plain,
    ! [X0] : join(zero,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f3472,f4160]) ).

fof(f4530,plain,
    ! [X0] : X0 = join(zero,complement(join(complement(X0),complement(X0)))),
    inference(paramodulation,[status(thm)],[f28,f371]) ).

fof(f4531,plain,
    ! [X0] : X0 = complement(join(complement(X0),complement(X0))),
    inference(forward_demodulation,[status(thm)],[f4161,f4530]) ).

fof(f4532,plain,
    ! [X0] : X0 = meet(X0,X0),
    inference(forward_demodulation,[status(thm)],[f19,f4531]) ).

fof(f4533,plain,
    ! [X0] : X0 = complement(complement(X0)),
    inference(forward_demodulation,[status(thm)],[f3046,f4532]) ).

fof(f4603,plain,
    ! [X0] : join(complement(complement(X0)),X0) = complement(complement(X0)),
    inference(paramodulation,[status(thm)],[f4533,f3007]) ).

fof(f4604,plain,
    ! [X0] : join(X0,complement(complement(X0))) = complement(complement(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f4603]) ).

fof(f4605,plain,
    ! [X0] : join(X0,X0) = complement(complement(X0)),
    inference(forward_demodulation,[status(thm)],[f4533,f4604]) ).

fof(f4606,plain,
    ! [X0] : join(X0,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f4533,f4605]) ).

fof(f4803,plain,
    ! [X0,X1] : join(X0,join(X0,X1)) = join(X1,X0),
    inference(paramodulation,[status(thm)],[f4606,f115]) ).

fof(f6210,plain,
    ! [X0,X1] : join(meet(X0,X1),X1) = join(meet(complement(X0),X1),meet(X0,X1)),
    inference(paramodulation,[status(thm)],[f640,f4803]) ).

fof(f6211,plain,
    ! [X0,X1] : join(X0,meet(X1,X0)) = join(meet(complement(X1),X0),meet(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f16,f6210]) ).

fof(f6212,plain,
    ! [X0,X1] : join(X0,meet(X1,X0)) = join(meet(X1,X0),meet(complement(X1),X0)),
    inference(forward_demodulation,[status(thm)],[f16,f6211]) ).

fof(f6213,plain,
    ! [X0,X1] : join(X0,meet(X1,X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f640,f6212]) ).

fof(f7919,plain,
    ! [X0,X1] : X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(top)),
    inference(paramodulation,[status(thm)],[f3639,f357]) ).

fof(f7920,plain,
    ! [X0,X1] : X0 = join(complement(top),meet(X0,join(complement(complement(X0)),X1))),
    inference(forward_demodulation,[status(thm)],[f16,f7919]) ).

fof(f7921,plain,
    ! [X0,X1] : X0 = join(zero,meet(X0,join(complement(complement(X0)),X1))),
    inference(forward_demodulation,[status(thm)],[f262,f7920]) ).

fof(f7922,plain,
    ! [X0,X1] : X0 = meet(X0,join(complement(complement(X0)),X1)),
    inference(forward_demodulation,[status(thm)],[f4161,f7921]) ).

fof(f7923,plain,
    ! [X0,X1] : X0 = meet(X0,join(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f4533,f7922]) ).

fof(f8824,plain,
    ! [X0,X1] : converse(X0) = meet(converse(X0),converse(join(X0,X1))),
    inference(paramodulation,[status(thm)],[f24,f7923]) ).

fof(f15643,plain,
    ! [X0,X1,X2] : converse(converse(composition(X0,X1))) = meet(converse(converse(composition(X0,X1))),converse(composition(join(converse(X1),X2),converse(X0)))),
    inference(paramodulation,[status(thm)],[f353,f8824]) ).

fof(f15644,plain,
    ! [X0,X1,X2] : composition(X0,X1) = meet(converse(converse(composition(X0,X1))),converse(composition(join(converse(X1),X2),converse(X0)))),
    inference(forward_demodulation,[status(thm)],[f23,f15643]) ).

fof(f15645,plain,
    ! [X0,X1,X2] : composition(X0,X1) = meet(composition(X0,X1),converse(composition(join(converse(X1),X2),converse(X0)))),
    inference(forward_demodulation,[status(thm)],[f23,f15644]) ).

fof(f15646,plain,
    ! [X0,X1,X2] : composition(X0,X1) = meet(composition(X0,X1),composition(X0,converse(join(converse(X1),X2)))),
    inference(forward_demodulation,[status(thm)],[f346,f15645]) ).

fof(f15647,plain,
    ! [X0,X1,X2] : composition(X0,X1) = meet(composition(X0,X1),composition(X0,join(X1,converse(X2)))),
    inference(forward_demodulation,[status(thm)],[f287,f15646]) ).

fof(f83515,plain,
    ! [X0,X1,X2] : composition(X0,X1) = meet(composition(X0,X1),composition(X0,join(X1,X2))),
    inference(paramodulation,[status(thm)],[f23,f15647]) ).

fof(f84522,plain,
    ! [X0] : composition(X0,sk0_0) = meet(composition(X0,sk0_0),composition(X0,sk0_1)),
    inference(paramodulation,[status(thm)],[f32,f83515]) ).

fof(f92670,plain,
    ! [X0] : join(composition(X0,sk0_1),composition(X0,sk0_0)) = composition(X0,sk0_1),
    inference(paramodulation,[status(thm)],[f84522,f6213]) ).

fof(f92671,plain,
    ! [X0] : join(composition(X0,sk0_0),composition(X0,sk0_1)) = composition(X0,sk0_1),
    inference(forward_demodulation,[status(thm)],[f16,f92670]) ).

fof(f93626,plain,
    ( composition(sk0_3,sk0_1) != composition(sk0_3,sk0_1)
    | spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f92671,f39]) ).

fof(f93627,plain,
    ( $false
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f93626]) ).

fof(f93628,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f93627]) ).

fof(f93629,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f40,f226,f93628]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : REL009+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n009.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Mon Apr 29 20:59:11 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.09/0.30  % Drodi V3.6.0
% 201.27/25.72  % Refutation found
% 201.27/25.72  % SZS status Theorem for theBenchmark: Theorem is valid
% 201.27/25.72  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 204.00/26.00  % Elapsed time: 25.672801 seconds
% 204.00/26.00  % CPU time: 203.125415 seconds
% 204.00/26.00  % Total memory used: 1.120 GB
% 204.00/26.00  % Net memory used: 1.106 GB
%------------------------------------------------------------------------------