TSTP Solution File: LCL516+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL516+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 : Sun May  5 07:46:15 EDT 2024

% Result   : Theorem 9.57s 1.71s
% Output   : Refutation 9.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  124 (  56 unt;   0 def)
%            Number of atoms       :  215 (  21 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  163 (  72   ~;  65   |;   2   &)
%                                         (  10 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   12 (  10 usr;  10 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  201 ( 197   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f42818,plain,
    $false,
    inference(resolution,[],[f42311,f122]) ).

fof(f122,plain,
    ~ is_a_theorem(implies(sK0,or(sK0,sK1))),
    inference(superposition,[],[f101,f115]) ).

fof(f115,plain,
    ! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
    inference(superposition,[],[f99,f98]) ).

fof(f98,plain,
    ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,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/sandbox/benchmark/theBenchmark.p',op_implies_and) ).

fof(f88,plain,
    op_equiv,
    inference(cnf_transformation,[],[f42]) ).

fof(f42,axiom,
    op_equiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_equiv) ).

fof(f87,plain,
    op_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f32,axiom,
    op_or,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_or) ).

fof(f86,plain,
    op_equiv,
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    op_equiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_equiv) ).

fof(f85,plain,
    op_or,
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    op_or,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).

fof(f84,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f33,axiom,
    op_implies_and,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).

fof(f83,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_modus_ponens) ).

fof(f82,plain,
    kn1,
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    kn1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).

fof(f81,plain,
    kn3,
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    kn3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).

fof(f80,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f79,plain,
    kn2,
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    kn2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).

fof(f78,plain,
    ~ cn2,
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ~ cn2,
    inference(flattening,[],[f44]) ).

fof(f44,negated_conjecture,
    ~ cn2,
    inference(negated_conjecture,[],[f43]) ).

fof(f43,conjecture,
    cn2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).

fof(f99,plain,
    ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,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/sandbox/benchmark/theBenchmark.p',op_or) ).

fof(f101,plain,
    ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1))),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92]) ).

fof(f92,plain,
    ( cn2
    | ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1))) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ( cn2
    | ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f69,f76]) ).

fof(f76,plain,
    ( ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(not(X0),X1)))
   => ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1))) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ( cn2
    | ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(not(X0),X1))) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f57,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
   => cn2 ),
    inference(unused_predicate_definition_removal,[],[f53]) ).

fof(f53,plain,
    ( cn2
  <=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ( cn2
  <=> ! [X3,X4] : is_a_theorem(implies(X3,implies(not(X3),X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).

fof(f100,plain,
    ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
      | ~ op_equiv ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
    | ~ op_equiv ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ( op_equiv
   => ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).

fof(f42311,plain,
    ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
    inference(resolution,[],[f42181,f25672]) ).

fof(f25672,plain,
    ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0))),
    inference(resolution,[],[f25533,f20558]) ).

fof(f20558,plain,
    ! [X0,X1] : is_a_theorem(or(not(X0),or(X0,X1))),
    inference(superposition,[],[f20476,f115]) ).

fof(f20476,plain,
    ! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
    inference(resolution,[],[f233,f103]) ).

fof(f103,plain,
    ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93,f102,f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ kn2 ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
    | ~ kn2 ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,plain,
    ( kn2
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(unused_predicate_definition_removal,[],[f55]) ).

fof(f55,plain,
    ( kn2
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ( kn2
  <=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).

fof(f102,plain,
    ! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93]) ).

fof(f93,plain,
    ! [X0] :
      ( is_a_theorem(implies(X0,and(X0,X0)))
      | ~ kn1 ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
    | ~ kn1 ),
    inference(ennf_transformation,[],[f60]) ).

fof(f60,plain,
    ( kn1
   => ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(unused_predicate_definition_removal,[],[f54]) ).

fof(f54,plain,
    ( kn1
  <=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ( kn1
  <=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).

fof(f233,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(implies(and(X0,not(X1)),X2))
      | is_a_theorem(or(X2,implies(X0,X1))) ),
    inference(superposition,[],[f223,f98]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( is_a_theorem(or(X0,not(X1)))
      | ~ is_a_theorem(implies(X1,X0)) ),
    inference(resolution,[],[f218,f198]) ).

fof(f198,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(or(X0,X1))
      | is_a_theorem(or(X2,X0))
      | ~ is_a_theorem(implies(X1,X2)) ),
    inference(resolution,[],[f188,f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(X0,X1))
      | is_a_theorem(X1)
      | ~ is_a_theorem(X0) ),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93,f102,f94,f103,f95,f104,f96]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f62]) ).

fof(f62,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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(equiv(X0,X1))
      | X0 = X1 ),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93,f102,f94,f103,f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ is_a_theorem(equiv(X0,X1))
      | ~ substitution_of_equivalents ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ is_a_theorem(equiv(X0,X1)) )
    | ~ substitution_of_equivalents ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,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/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f188,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),or(X1,X2)))
      | ~ is_a_theorem(or(X2,X0)) ),
    inference(resolution,[],[f180,f105]) ).

fof(f180,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
    inference(forward_demodulation,[],[f179,f115]) ).

fof(f179,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X0),or(X0,X1)))),
    inference(forward_demodulation,[],[f175,f118]) ).

fof(f118,plain,
    ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
    inference(forward_demodulation,[],[f111,f98]) ).

fof(f111,plain,
    ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
    inference(superposition,[],[f99,f98]) ).

fof(f175,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,not(X0)),or(X0,X1)))),
    inference(superposition,[],[f169,f99]) ).

fof(f169,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
    inference(forward_demodulation,[],[f106,f115]) ).

fof(f106,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
    inference(global_subsumption,[],[f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93,f102,f94,f103,f95,f104,f96,f105,f97]) ).

fof(f97,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
      | ~ kn3 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
    | ~ kn3 ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,plain,
    ( kn3
   => ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    inference(unused_predicate_definition_removal,[],[f56]) ).

fof(f56,plain,
    ( kn3
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ( kn3
  <=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).

fof(f218,plain,
    ! [X0] : is_a_theorem(or(not(X0),X0)),
    inference(resolution,[],[f215,f103]) ).

fof(f215,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(and(not(X1),not(X1)),X0))
      | is_a_theorem(or(X0,X1)) ),
    inference(resolution,[],[f198,f123]) ).

fof(f123,plain,
    ! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
    inference(superposition,[],[f102,f115]) ).

fof(f25533,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(or(X0,X1))
      | is_a_theorem(or(X1,X0)) ),
    inference(resolution,[],[f25457,f19681]) ).

fof(f19681,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(or(X2,not(X0)))
      | ~ is_a_theorem(or(X0,X1))
      | is_a_theorem(or(X1,X2)) ),
    inference(forward_demodulation,[],[f19666,f115]) ).

fof(f19666,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(or(X0,X1))
      | is_a_theorem(implies(not(X1),X2))
      | ~ is_a_theorem(or(X2,not(X0))) ),
    inference(superposition,[],[f192,f99]) ).

fof(f192,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(not(and(X1,X2)))
      | is_a_theorem(implies(X2,X0))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(resolution,[],[f181,f124]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(or(X0,X1))
      | is_a_theorem(X1)
      | ~ is_a_theorem(not(X0)) ),
    inference(superposition,[],[f105,f115]) ).

fof(f181,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(or(and(X0,X1),implies(X1,X2)))
      | ~ is_a_theorem(or(X2,X0)) ),
    inference(resolution,[],[f178,f105]) ).

fof(f178,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
    inference(forward_demodulation,[],[f174,f115]) ).

fof(f174,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
    inference(superposition,[],[f169,f98]) ).

fof(f25457,plain,
    ! [X0] : is_a_theorem(or(X0,not(X0))),
    inference(resolution,[],[f24543,f20558]) ).

fof(f24543,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(or(X1,or(X0,X1)))
      | is_a_theorem(or(X0,X1)) ),
    inference(resolution,[],[f24416,f21348]) ).

fof(f21348,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(or(or(X0,X1),X2))
      | ~ is_a_theorem(or(X1,X2)) ),
    inference(resolution,[],[f20530,f188]) ).

fof(f20530,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(implies(implies(X1,X2),X0))
      | is_a_theorem(or(X0,X1)) ),
    inference(resolution,[],[f20476,f198]) ).

fof(f24416,plain,
    ! [X0] :
      ( ~ is_a_theorem(or(X0,X0))
      | is_a_theorem(X0) ),
    inference(duplicate_literal_removal,[],[f24362]) ).

fof(f24362,plain,
    ! [X0] :
      ( ~ is_a_theorem(or(X0,X0))
      | is_a_theorem(X0)
      | ~ is_a_theorem(or(X0,X0)) ),
    inference(resolution,[],[f24317,f19689]) ).

fof(f19689,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(or(X0,not(X1)))
      | is_a_theorem(X0)
      | ~ is_a_theorem(or(X1,X1)) ),
    inference(resolution,[],[f19652,f105]) ).

fof(f19652,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(or(X0,X0),X1))
      | ~ is_a_theorem(or(X1,not(X0))) ),
    inference(resolution,[],[f192,f558]) ).

fof(f558,plain,
    ! [X0] : is_a_theorem(not(and(not(X0),or(X0,X0)))),
    inference(superposition,[],[f102,f117]) ).

fof(f117,plain,
    ! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
    inference(superposition,[],[f98,f99]) ).

fof(f24317,plain,
    ! [X0] :
      ( is_a_theorem(or(X0,not(X0)))
      | ~ is_a_theorem(or(X0,X0)) ),
    inference(resolution,[],[f21426,f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(equiv(not(X0),X1))
      | is_a_theorem(or(X0,X1)) ),
    inference(resolution,[],[f137,f105]) ).

fof(f137,plain,
    ! [X0,X1] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
    inference(superposition,[],[f133,f115]) ).

fof(f133,plain,
    ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
    inference(superposition,[],[f103,f100]) ).

fof(f21426,plain,
    ! [X0] :
      ( is_a_theorem(equiv(not(X0),not(X0)))
      | ~ is_a_theorem(or(X0,X0)) ),
    inference(resolution,[],[f21343,f19689]) ).

fof(f21343,plain,
    ! [X0] : is_a_theorem(or(equiv(X0,X0),X0)),
    inference(resolution,[],[f20530,f131]) ).

fof(f131,plain,
    ! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
    inference(superposition,[],[f102,f100]) ).

fof(f42181,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(or(X1,not(X0)))
      | is_a_theorem(implies(X0,X1)) ),
    inference(resolution,[],[f42129,f192]) ).

fof(f42129,plain,
    ! [X0] : is_a_theorem(not(and(not(X0),X0))),
    inference(resolution,[],[f33217,f102]) ).

fof(f33217,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(implies(X1,and(X0,X2)))
      | is_a_theorem(not(and(not(X0),X1))) ),
    inference(resolution,[],[f2315,f103]) ).

fof(f2315,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(implies(X1,X2))
      | is_a_theorem(not(and(not(X2),X0)))
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(resolution,[],[f359,f105]) ).

fof(f359,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),not(and(not(X1),X2))))
      | ~ is_a_theorem(implies(X2,X0)) ),
    inference(superposition,[],[f170,f118]) ).

fof(f170,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(or(and(X0,X1),not(and(X1,X2))))
      | ~ is_a_theorem(implies(X2,X0)) ),
    inference(resolution,[],[f169,f105]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : LCL516+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri May  3 13:34:25 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (12536)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (12540)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  TRYING [1]
% 0.13/0.36  TRYING [2]
% 0.13/0.36  TRYING [3]
% 0.13/0.36  % (12539)WARNING: value z3 for option sas not known
% 0.13/0.36  % (12537)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  % (12538)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (12539)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36  % (12541)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36  % (12542)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.36  % (12543)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.37  TRYING [4]
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2]
% 0.13/0.38  TRYING [3]
% 0.13/0.41  TRYING [4]
% 0.20/0.42  TRYING [5]
% 2.57/0.76  TRYING [5]
% 7.38/1.46  TRYING [6]
% 7.97/1.46  TRYING [1]
% 7.97/1.46  TRYING [2]
% 7.97/1.47  TRYING [3]
% 7.97/1.47  TRYING [4]
% 8.41/1.53  TRYING [5]
% 9.57/1.71  % (12539)First to succeed.
% 9.57/1.71  % (12539)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12536"
% 9.57/1.71  % (12539)Refutation found. Thanks to Tanya!
% 9.57/1.71  % SZS status Theorem for theBenchmark
% 9.57/1.71  % SZS output start Proof for theBenchmark
% See solution above
% 9.57/1.71  % (12539)------------------------------
% 9.57/1.71  % (12539)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 9.57/1.71  % (12539)Termination reason: Refutation
% 9.57/1.71  
% 9.57/1.71  % (12539)Memory used [KB]: 25335
% 9.57/1.71  % (12539)Time elapsed: 1.345 s
% 9.57/1.71  % (12539)Instructions burned: 4367 (million)
% 9.57/1.71  % (12536)Success in time 1.337 s
%------------------------------------------------------------------------------