TSTP Solution File: LCL528+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n007.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 : Thu Aug 31 08:24:27 EDT 2023

% Result   : Theorem 20.49s 3.26s
% Output   : Refutation 20.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   44
%            Number of leaves      :   33
% Syntax   : Number of formulae    :  195 ( 115 unt;   0 def)
%            Number of atoms       :  298 (  64 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  176 (  73   ~;  65   |;   2   &)
%                                         (  13 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   19 (  17 usr;  17 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-2 aty)
%            Number of variables   :  290 (; 286   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f172866,plain,
    $false,
    inference(subsumption_resolution,[],[f171894,f12479]) ).

fof(f12479,plain,
    ! [X0] : is_a_theorem(implies(X0,X0)),
    inference(superposition,[],[f217,f11530]) ).

fof(f11530,plain,
    ! [X14,X13] : implies(X13,X14) = implies(X13,implies(X13,X14)),
    inference(subsumption_resolution,[],[f11460,f217]) ).

fof(f11460,plain,
    ! [X14,X13] :
      ( implies(X13,X14) = implies(X13,implies(X13,X14))
      | ~ is_a_theorem(implies(implies(X13,X14),implies(X13,implies(X13,X14)))) ),
    inference(resolution,[],[f2822,f304]) ).

fof(f304,plain,
    ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
    inference(subsumption_resolution,[],[f206,f173]) ).

fof(f173,plain,
    implies_2,
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    implies_2,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_implies_2) ).

fof(f206,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
      | ~ implies_2 ),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
    | ~ implies_2 ),
    inference(ennf_transformation,[],[f120]) ).

fof(f120,plain,
    ( implies_2
   => ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f5]) ).

fof(f5,axiom,
    ( implies_2
  <=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',implies_2) ).

fof(f2822,plain,
    ! [X6,X7] :
      ( ~ is_a_theorem(implies(X7,X6))
      | X6 = X7
      | ~ is_a_theorem(implies(X6,X7)) ),
    inference(resolution,[],[f473,f478]) ).

fof(f478,plain,
    ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
    inference(subsumption_resolution,[],[f208,f164]) ).

fof(f164,plain,
    equivalence_3,
    inference(cnf_transformation,[],[f48]) ).

fof(f48,axiom,
    equivalence_3,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_equivalence_3) ).

fof(f208,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
      | ~ equivalence_3 ),
    inference(cnf_transformation,[],[f150]) ).

fof(f150,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
    | ~ equivalence_3 ),
    inference(ennf_transformation,[],[f110]) ).

fof(f110,plain,
    ( equivalence_3
   => ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

fof(f15,axiom,
    ( equivalence_3
  <=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',equivalence_3) ).

fof(f473,plain,
    ! [X10,X11,X8,X9] :
      ( ~ is_a_theorem(implies(X11,implies(X8,equiv(X9,X10))))
      | X9 = X10
      | ~ is_a_theorem(X8)
      | ~ is_a_theorem(X11) ),
    inference(resolution,[],[f233,f232]) ).

fof(f232,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0) ),
    inference(subsumption_resolution,[],[f210,f176]) ).

fof(f176,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_modus_ponens) ).

fof(f210,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f152]) ).

fof(f152,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f124]) ).

fof(f124,plain,
    ( modus_ponens
   => ! [X0,X1] :
        ( ( is_a_theorem(implies(X0,X1))
          & is_a_theorem(X0) )
       => is_a_theorem(X1) ) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

fof(f1,axiom,
    ( modus_ponens
  <=> ! [X0,X1] :
        ( ( is_a_theorem(implies(X0,X1))
          & is_a_theorem(X0) )
       => is_a_theorem(X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',modus_ponens) ).

fof(f233,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(implies(X0,equiv(X1,X2)))
      | ~ is_a_theorem(X0)
      | X1 = X2 ),
    inference(resolution,[],[f232,f223]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(equiv(X0,X1))
      | X0 = X1 ),
    inference(subsumption_resolution,[],[f209,f163]) ).

fof(f163,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f49]) ).

fof(f49,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',substitution_of_equivalents) ).

fof(f209,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ is_a_theorem(equiv(X0,X1))
      | ~ substitution_of_equivalents ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ is_a_theorem(equiv(X0,X1)) )
    | ~ substitution_of_equivalents ),
    inference(ennf_transformation,[],[f123]) ).

fof(f123,plain,
    ( substitution_of_equivalents
   => ! [X0,X1] :
        ( is_a_theorem(equiv(X0,X1))
       => X0 = X1 ) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f2,axiom,
    ( substitution_of_equivalents
  <=> ! [X0,X1] :
        ( is_a_theorem(equiv(X0,X1))
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',substitution_of_equivalents) ).

fof(f217,plain,
    ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
    inference(subsumption_resolution,[],[f199,f174]) ).

fof(f174,plain,
    implies_1,
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    implies_1,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_implies_1) ).

fof(f199,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X0,implies(X1,X0)))
      | ~ implies_1 ),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
    | ~ implies_1 ),
    inference(ennf_transformation,[],[f121]) ).

fof(f121,plain,
    ( implies_1
   => ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

fof(f4,axiom,
    ( implies_1
  <=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',implies_1) ).

fof(f171894,plain,
    ~ is_a_theorem(implies(and(sK0,sK1),and(sK0,sK1))),
    inference(backward_demodulation,[],[f228,f171547]) ).

fof(f171547,plain,
    ! [X2,X3] : and(X3,X2) = and(X2,X3),
    inference(superposition,[],[f154006,f118504]) ).

fof(f118504,plain,
    ! [X698,X699] : and(X698,X699) = not(implies(X698,not(X699))),
    inference(superposition,[],[f87505,f89089]) ).

fof(f89089,plain,
    ! [X8,X7] : implies(X8,not(X7)) = not(and(X8,X7)),
    inference(forward_demodulation,[],[f88785,f12774]) ).

fof(f12774,plain,
    ! [X8] : and(X8,X8) = X8,
    inference(subsumption_resolution,[],[f12767,f218]) ).

fof(f218,plain,
    ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
    inference(subsumption_resolution,[],[f200,f171]) ).

fof(f171,plain,
    and_1,
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    and_1,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_and_1) ).

fof(f200,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ and_1 ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
    | ~ and_1 ),
    inference(ennf_transformation,[],[f118]) ).

fof(f118,plain,
    ( and_1
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(unused_predicate_definition_removal,[],[f7]) ).

fof(f7,axiom,
    ( and_1
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',and_1) ).

fof(f12767,plain,
    ! [X8] :
      ( and(X8,X8) = X8
      | ~ is_a_theorem(implies(and(X8,X8),X8)) ),
    inference(resolution,[],[f12481,f2822]) ).

fof(f12481,plain,
    ! [X4] : is_a_theorem(implies(X4,and(X4,X4))),
    inference(superposition,[],[f229,f11530]) ).

fof(f229,plain,
    ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
    inference(subsumption_resolution,[],[f202,f169]) ).

fof(f169,plain,
    and_3,
    inference(cnf_transformation,[],[f42]) ).

fof(f42,axiom,
    and_3,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_and_3) ).

fof(f202,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
      | ~ and_3 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
    | ~ and_3 ),
    inference(ennf_transformation,[],[f116]) ).

fof(f116,plain,
    ( and_3
   => ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    inference(unused_predicate_definition_removal,[],[f9]) ).

fof(f9,axiom,
    ( and_3
  <=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',and_3) ).

fof(f88785,plain,
    ! [X8,X7] : implies(X8,and(not(X7),not(X7))) = not(and(X8,X7)),
    inference(superposition,[],[f241,f87646]) ).

fof(f87646,plain,
    ! [X33] : implies(not(X33),X33) = X33,
    inference(backward_demodulation,[],[f12801,f87505]) ).

fof(f12801,plain,
    ! [X33] : implies(not(X33),X33) = not(not(X33)),
    inference(superposition,[],[f239,f12774]) ).

fof(f239,plain,
    ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
    inference(subsumption_resolution,[],[f188,f178]) ).

fof(f178,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f33,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_op_implies_and) ).

fof(f188,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
    | ~ op_implies_and ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ( op_implies_and
   => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',op_implies_and) ).

fof(f241,plain,
    ! [X2,X3,X4] : implies(X4,and(X2,not(X3))) = not(and(X4,implies(X2,X3))),
    inference(superposition,[],[f239,f239]) ).

fof(f87505,plain,
    ! [X0] : not(not(X0)) = X0,
    inference(resolution,[],[f87444,f13598]) ).

fof(f13598,plain,
    ! [X0] :
      ( ~ is_a_theorem(or(not(X0),X0))
      | not(not(X0)) = X0 ),
    inference(forward_demodulation,[],[f13570,f256]) ).

fof(f256,plain,
    ! [X2,X3] : implies(not(X2),X3) = or(X2,X3),
    inference(superposition,[],[f249,f239]) ).

fof(f249,plain,
    ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
    inference(subsumption_resolution,[],[f191,f181]) ).

fof(f181,plain,
    op_or,
    inference(cnf_transformation,[],[f83]) ).

fof(f83,axiom,
    op_or,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',s1_0_op_or) ).

fof(f191,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
    | ~ op_or ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,axiom,
    ( op_or
   => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',op_or) ).

fof(f13570,plain,
    ! [X0] :
      ( not(not(X0)) = X0
      | ~ is_a_theorem(implies(not(not(X0)),X0)) ),
    inference(resolution,[],[f13329,f2822]) ).

fof(f13329,plain,
    ! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
    inference(superposition,[],[f215,f13016]) ).

fof(f13016,plain,
    ! [X285] : or(X285,X285) = not(not(X285)),
    inference(superposition,[],[f249,f12774]) ).

fof(f215,plain,
    ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
    inference(subsumption_resolution,[],[f197,f168]) ).

fof(f168,plain,
    or_1,
    inference(cnf_transformation,[],[f43]) ).

fof(f43,axiom,
    or_1,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_or_1) ).

fof(f197,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X0,or(X0,X1)))
      | ~ or_1 ),
    inference(cnf_transformation,[],[f139]) ).

fof(f139,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
    | ~ or_1 ),
    inference(ennf_transformation,[],[f115]) ).

fof(f115,plain,
    ( or_1
   => ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f10]) ).

fof(f10,axiom,
    ( or_1
  <=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',or_1) ).

fof(f87444,plain,
    ! [X92] : is_a_theorem(or(not(X92),X92)),
    inference(forward_demodulation,[],[f87443,f11549]) ).

fof(f11549,plain,
    ! [X120,X121] : or(X120,X121) = or(X120,or(X120,X121)),
    inference(subsumption_resolution,[],[f11501,f216]) ).

fof(f216,plain,
    ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
    inference(subsumption_resolution,[],[f198,f177]) ).

fof(f177,plain,
    or_2,
    inference(cnf_transformation,[],[f44]) ).

fof(f44,axiom,
    or_2,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_or_2) ).

fof(f198,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X1,or(X0,X1)))
      | ~ or_2 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
    | ~ or_2 ),
    inference(ennf_transformation,[],[f114]) ).

fof(f114,plain,
    ( or_2
   => ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f11]) ).

fof(f11,axiom,
    ( or_2
  <=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',or_2) ).

fof(f11501,plain,
    ! [X120,X121] :
      ( or(X120,X121) = or(X120,or(X120,X121))
      | ~ is_a_theorem(implies(or(X120,X121),or(X120,or(X120,X121)))) ),
    inference(resolution,[],[f2822,f337]) ).

fof(f337,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
    inference(forward_demodulation,[],[f335,f256]) ).

fof(f335,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X0,implies(not(X0),X1)),implies(not(X0),X1))),
    inference(superposition,[],[f304,f256]) ).

fof(f87443,plain,
    ! [X92] : is_a_theorem(or(not(X92),or(not(X92),X92))),
    inference(forward_demodulation,[],[f87442,f256]) ).

fof(f87442,plain,
    ! [X92] : is_a_theorem(or(not(X92),implies(not(not(X92)),X92))),
    inference(forward_demodulation,[],[f87290,f239]) ).

fof(f87290,plain,
    ! [X92] : is_a_theorem(or(not(X92),not(and(not(not(X92)),not(X92))))),
    inference(superposition,[],[f1153,f85776]) ).

fof(f85776,plain,
    ! [X17] : not(X17) = or(not(X17),not(X17)),
    inference(superposition,[],[f17202,f85636]) ).

fof(f85636,plain,
    ! [X0] : not(X0) = not(not(not(X0))),
    inference(resolution,[],[f85345,f13598]) ).

fof(f85345,plain,
    ! [X33] : is_a_theorem(or(not(not(X33)),not(X33))),
    inference(forward_demodulation,[],[f85344,f256]) ).

fof(f85344,plain,
    ! [X33] : is_a_theorem(implies(not(not(not(X33))),not(X33))),
    inference(forward_demodulation,[],[f85343,f239]) ).

fof(f85343,plain,
    ! [X33] : is_a_theorem(not(and(not(not(not(X33))),not(not(X33))))),
    inference(forward_demodulation,[],[f85342,f13016]) ).

fof(f85342,plain,
    ! [X33] : is_a_theorem(not(and(not(not(not(X33))),or(X33,X33)))),
    inference(forward_demodulation,[],[f85272,f255]) ).

fof(f255,plain,
    ! [X6,X7,X5] : or(X7,and(not(X5),not(X6))) = not(and(not(X7),or(X5,X6))),
    inference(superposition,[],[f249,f249]) ).

fof(f85272,plain,
    ! [X33] : is_a_theorem(or(not(not(X33)),and(not(X33),not(X33)))),
    inference(superposition,[],[f85204,f12801]) ).

fof(f85204,plain,
    ! [X99,X100] : is_a_theorem(or(implies(X99,X100),and(X99,not(X100)))),
    inference(forward_demodulation,[],[f85203,f11549]) ).

fof(f85203,plain,
    ! [X99,X100] : is_a_theorem(or(implies(X99,X100),or(implies(X99,X100),and(X99,not(X100))))),
    inference(forward_demodulation,[],[f85202,f256]) ).

fof(f85202,plain,
    ! [X99,X100] : is_a_theorem(or(implies(X99,X100),implies(not(implies(X99,X100)),and(X99,not(X100))))),
    inference(forward_demodulation,[],[f85099,f241]) ).

fof(f85099,plain,
    ! [X99,X100] : is_a_theorem(or(implies(X99,X100),not(and(not(implies(X99,X100)),implies(X99,X100))))),
    inference(superposition,[],[f1153,f80398]) ).

fof(f80398,plain,
    ! [X213,X214] : implies(X213,X214) = or(implies(X213,X214),implies(X213,X214)),
    inference(superposition,[],[f11549,f80085]) ).

fof(f80085,plain,
    ! [X0,X1] : implies(X0,X1) = or(implies(X0,X1),not(X0)),
    inference(resolution,[],[f12494,f11454]) ).

fof(f11454,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(or(X0,X1),X0))
      | or(X0,X1) = X0 ),
    inference(resolution,[],[f2822,f215]) ).

fof(f12494,plain,
    ! [X26,X25] : is_a_theorem(implies(or(implies(X25,X26),not(X25)),implies(X25,X26))),
    inference(superposition,[],[f280,f11530]) ).

fof(f280,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
    inference(forward_demodulation,[],[f279,f256]) ).

fof(f279,plain,
    ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
    inference(subsumption_resolution,[],[f205,f175]) ).

fof(f175,plain,
    modus_tollens,
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    modus_tollens,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_modus_tollens) ).

fof(f205,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
      | ~ modus_tollens ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
    | ~ modus_tollens ),
    inference(ennf_transformation,[],[f122]) ).

fof(f122,plain,
    ( modus_tollens
   => ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f3]) ).

fof(f3,axiom,
    ( modus_tollens
  <=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',modus_tollens) ).

fof(f17202,plain,
    ! [X3] : not(not(X3)) = or(X3,not(not(X3))),
    inference(superposition,[],[f11549,f13016]) ).

fof(f1153,plain,
    ! [X2,X3] : is_a_theorem(or(X3,not(and(not(X2),or(X3,X2))))),
    inference(forward_demodulation,[],[f1115,f256]) ).

fof(f1115,plain,
    ! [X2,X3] : is_a_theorem(implies(not(X3),not(and(not(X2),or(X3,X2))))),
    inference(superposition,[],[f229,f259]) ).

fof(f259,plain,
    ! [X6,X7,X5] : implies(X7,and(not(X5),not(X6))) = not(and(X7,or(X5,X6))),
    inference(superposition,[],[f239,f249]) ).

fof(f154006,plain,
    ! [X176,X177] : and(X176,X177) = not(implies(X177,not(X176))),
    inference(superposition,[],[f87505,f135534]) ).

fof(f135534,plain,
    ! [X0,X1] : implies(X1,not(X0)) = not(and(X0,X1)),
    inference(superposition,[],[f121565,f87505]) ).

fof(f121565,plain,
    ! [X14,X15] : implies(X14,X15) = not(and(not(X15),X14)),
    inference(superposition,[],[f121208,f87646]) ).

fof(f121208,plain,
    ! [X2,X3,X4] : not(and(not(X4),implies(X2,X3))) = implies(implies(X2,X3),X4),
    inference(forward_demodulation,[],[f120817,f101077]) ).

fof(f101077,plain,
    ! [X10,X9] : implies(X9,X10) = or(X10,not(X9)),
    inference(superposition,[],[f87771,f88600]) ).

fof(f88600,plain,
    ! [X0,X1] : or(X0,X1) = or(X1,X0),
    inference(subsumption_resolution,[],[f88539,f87643]) ).

fof(f87643,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X1,X0),or(X0,X1))),
    inference(backward_demodulation,[],[f294,f87505]) ).

fof(f294,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X1,not(not(X0))),or(X0,X1))),
    inference(superposition,[],[f280,f256]) ).

fof(f88539,plain,
    ! [X0,X1] :
      ( or(X0,X1) = or(X1,X0)
      | ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(resolution,[],[f87643,f2822]) ).

fof(f87771,plain,
    ! [X29,X30] : implies(X29,X30) = or(not(X29),X30),
    inference(superposition,[],[f256,f87505]) ).

fof(f120817,plain,
    ! [X2,X3,X4] : not(and(not(X4),implies(X2,X3))) = or(X4,not(implies(X2,X3))),
    inference(backward_demodulation,[],[f254,f118948]) ).

fof(f118948,plain,
    ! [X14,X15] : and(X14,not(X15)) = not(implies(X14,X15)),
    inference(forward_demodulation,[],[f118947,f85718]) ).

fof(f85718,plain,
    ! [X0] : not(X0) = implies(X0,not(X0)),
    inference(backward_demodulation,[],[f49905,f85636]) ).

fof(f49905,plain,
    ! [X0] : not(not(not(X0))) = implies(X0,not(X0)),
    inference(subsumption_resolution,[],[f49904,f13522]) ).

fof(f13522,plain,
    ! [X80] : is_a_theorem(or(not(not(X80)),implies(X80,not(X80)))),
    inference(forward_demodulation,[],[f13379,f256]) ).

fof(f13379,plain,
    ! [X80] : is_a_theorem(implies(not(not(not(X80))),implies(X80,not(X80)))),
    inference(superposition,[],[f280,f13016]) ).

fof(f49904,plain,
    ! [X0] :
      ( ~ is_a_theorem(or(not(not(X0)),implies(X0,not(X0))))
      | not(not(not(X0))) = implies(X0,not(X0)) ),
    inference(forward_demodulation,[],[f49858,f256]) ).

fof(f49858,plain,
    ! [X0] :
      ( not(not(not(X0))) = implies(X0,not(X0))
      | ~ is_a_theorem(implies(not(not(not(X0))),implies(X0,not(X0)))) ),
    inference(resolution,[],[f18718,f2822]) ).

fof(f18718,plain,
    ! [X3] : is_a_theorem(implies(implies(X3,not(X3)),not(not(not(X3))))),
    inference(superposition,[],[f13476,f13016]) ).

fof(f13476,plain,
    ! [X21,X22] : is_a_theorem(implies(implies(X21,X22),or(not(X21),X22))),
    inference(forward_demodulation,[],[f13475,f256]) ).

fof(f13475,plain,
    ! [X21,X22] : is_a_theorem(implies(implies(X21,X22),implies(not(not(X21)),X22))),
    inference(forward_demodulation,[],[f13346,f11530]) ).

fof(f13346,plain,
    ! [X21,X22] : is_a_theorem(implies(implies(X21,X22),implies(implies(X21,X22),implies(not(not(X21)),X22)))),
    inference(superposition,[],[f568,f13016]) ).

fof(f568,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
    inference(subsumption_resolution,[],[f212,f167]) ).

fof(f167,plain,
    or_3,
    inference(cnf_transformation,[],[f45]) ).

fof(f45,axiom,
    or_3,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_or_3) ).

fof(f212,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
      | ~ or_3 ),
    inference(cnf_transformation,[],[f155]) ).

fof(f155,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
    | ~ or_3 ),
    inference(ennf_transformation,[],[f113]) ).

fof(f113,plain,
    ( or_3
   => ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
    inference(unused_predicate_definition_removal,[],[f12]) ).

fof(f12,axiom,
    ( or_3
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',or_3) ).

fof(f118947,plain,
    ! [X14,X15] : and(X14,not(X15)) = implies(implies(X14,X15),not(implies(X14,X15))),
    inference(forward_demodulation,[],[f118717,f239]) ).

fof(f118717,plain,
    ! [X14,X15] : and(X14,not(X15)) = implies(not(and(X14,not(X15))),not(implies(X14,X15))),
    inference(superposition,[],[f118262,f87646]) ).

fof(f118262,plain,
    ! [X2,X3,X4] : implies(X4,and(X2,not(X3))) = implies(X4,not(implies(X2,X3))),
    inference(backward_demodulation,[],[f241,f89089]) ).

fof(f254,plain,
    ! [X2,X3,X4] : or(X4,and(X2,not(X3))) = not(and(not(X4),implies(X2,X3))),
    inference(superposition,[],[f249,f239]) ).

fof(f228,plain,
    ~ is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0))),
    inference(resolution,[],[f225,f227]) ).

fof(f227,plain,
    ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
    inference(subsumption_resolution,[],[f193,f158]) ).

fof(f158,plain,
    ~ axiom_m1,
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ~ axiom_m1,
    inference(flattening,[],[f89]) ).

fof(f89,negated_conjecture,
    ~ axiom_m1,
    inference(negated_conjecture,[],[f88]) ).

fof(f88,conjecture,
    axiom_m1,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',s1_0_axiom_m1) ).

fof(f193,plain,
    ( axiom_m1
    | ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f157,plain,
    ( axiom_m1
    | ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f135,f156]) ).

fof(f156,plain,
    ( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
   => ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( axiom_m1
    | ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
    inference(ennf_transformation,[],[f105]) ).

fof(f105,plain,
    ( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
   => axiom_m1 ),
    inference(unused_predicate_definition_removal,[],[f63]) ).

fof(f63,axiom,
    ( axiom_m1
  <=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',axiom_m1) ).

fof(f225,plain,
    ! [X0,X1] :
      ( is_a_theorem(strict_implies(X0,X1))
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(superposition,[],[f214,f224]) ).

fof(f224,plain,
    ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
    inference(subsumption_resolution,[],[f187,f180]) ).

fof(f180,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f85]) ).

fof(f85,axiom,
    op_strict_implies,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',s1_0_op_strict_implies) ).

fof(f187,plain,
    ! [X0,X1] :
      ( strict_implies(X0,X1) = necessarily(implies(X0,X1))
      | ~ op_strict_implies ),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
    | ~ op_strict_implies ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ( op_strict_implies
   => ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',op_strict_implies) ).

fof(f214,plain,
    ! [X0] :
      ( is_a_theorem(necessarily(X0))
      | ~ is_a_theorem(X0) ),
    inference(subsumption_resolution,[],[f196,f162]) ).

fof(f162,plain,
    necessitation,
    inference(cnf_transformation,[],[f78]) ).

fof(f78,axiom,
    necessitation,
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',km5_necessitation) ).

fof(f196,plain,
    ! [X0] :
      ( is_a_theorem(necessarily(X0))
      | ~ is_a_theorem(X0)
      | ~ necessitation ),
    inference(cnf_transformation,[],[f138]) ).

fof(f138,plain,
    ( ! [X0] :
        ( is_a_theorem(necessarily(X0))
        | ~ is_a_theorem(X0) )
    | ~ necessitation ),
    inference(ennf_transformation,[],[f109]) ).

fof(f109,plain,
    ( necessitation
   => ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    inference(unused_predicate_definition_removal,[],[f50]) ).

fof(f50,axiom,
    ( necessitation
  <=> ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',necessitation) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.33  % Computer : n007.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Thu Aug 24 19:12:25 EDT 2023
% 0.14/0.33  % CPUTime    : 
% 0.14/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.34  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882
% 0.14/0.34  % (26993)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (26998)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.20/0.40  % (26996)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.20/0.40  % (26999)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.20/0.40  % (27000)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.20/0.40  % (26995)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.20/0.40  % (26997)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.20/0.40  % (26994)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.20/0.40  % (26997)Refutation not found, incomplete strategy% (26997)------------------------------
% 0.20/0.40  % (26997)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.40  % (26997)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.40  % (26997)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.40  
% 0.20/0.40  % (26997)Memory used [KB]: 5628
% 0.20/0.40  % (26997)Time elapsed: 0.003 s
% 0.20/0.40  % (26997)------------------------------
% 0.20/0.40  % (26997)------------------------------
% 0.20/0.46  % (27001)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_401 on Vampire---4 for (401ds/0Mi)
% 20.12/3.24  % (27001)First to succeed.
% 20.49/3.26  % (27001)Refutation found. Thanks to Tanya!
% 20.49/3.26  % SZS status Theorem for Vampire---4
% 20.49/3.26  % SZS output start Proof for Vampire---4
% See solution above
% 20.49/3.26  % (27001)------------------------------
% 20.49/3.26  % (27001)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 20.49/3.26  % (27001)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 20.49/3.26  % (27001)Termination reason: Refutation
% 20.49/3.26  
% 20.49/3.26  % (27001)Memory used [KB]: 112322
% 20.49/3.26  % (27001)Time elapsed: 2.778 s
% 20.49/3.26  % (27001)------------------------------
% 20.49/3.26  % (27001)------------------------------
% 20.49/3.26  % (26993)Success in time 2.851 s
% 20.49/3.26  % Vampire---4.8 exiting
%------------------------------------------------------------------------------