TSTP Solution File: LCL500+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL500+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 : n023.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 13:42:35 EDT 2024

% Result   : Theorem 3.72s 0.88s
% Output   : Refutation 3.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  117 (  59 unt;   0 def)
%            Number of atoms       :  191 (  31 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  123 (  49   ~;  43   |;   2   &)
%                                         (  12 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   16 (  14 usr;  14 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  174 ( 170   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12649,plain,
    $false,
    inference(resolution,[],[f12640,f115]) ).

fof(f115,plain,
    ~ is_a_theorem(implies(and(sK0,sK1),sK0)),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100,f113,f101,f114,f102]) ).

fof(f102,plain,
    ( kn2
    | ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ( kn2
    | ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f72,f81]) ).

fof(f81,plain,
    ( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0))
   => ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ( kn2
    | ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f64,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
   => kn2 ),
    inference(unused_predicate_definition_removal,[],[f53]) ).

fof(f53,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/sandbox2/benchmark/theBenchmark.p',kn2) ).

fof(f114,plain,
    ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100,f113,f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
      | ~ op_equiv ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,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/sandbox2/benchmark/theBenchmark.p',op_equiv) ).

fof(f113,plain,
    ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,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/benchmark/theBenchmark.p',op_or) ).

fof(f112,plain,
    ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( and(X0,X1) = not(or(not(X0),not(X1)))
      | ~ op_and ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
    | ~ op_and ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ( op_and
   => ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and) ).

fof(f111,plain,
    ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,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/benchmark/theBenchmark.p',op_implies_and) ).

fof(f110,plain,
    ! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = or(not(X0),X1)
      | ~ op_implies_or ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
    | ~ op_implies_or ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ( op_implies_or
   => ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).

fof(f96,plain,
    op_equiv,
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).

fof(f95,plain,
    op_equiv,
    inference(cnf_transformation,[],[f44]) ).

fof(f44,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_equiv) ).

fof(f94,plain,
    op_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f33,axiom,
    op_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).

fof(f93,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f32,axiom,
    op_implies_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).

fof(f92,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f43]) ).

fof(f43,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_implies_and) ).

fof(f91,plain,
    op_or,
    inference(cnf_transformation,[],[f42]) ).

fof(f42,axiom,
    op_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).

fof(f90,plain,
    r1,
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    r1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).

fof(f89,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f88,plain,
    r2,
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    r2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).

fof(f87,plain,
    r3,
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    r3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).

fof(f86,plain,
    r5,
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    r5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r5) ).

fof(f85,plain,
    r4,
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    r4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).

fof(f84,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_modus_ponens) ).

fof(f83,plain,
    ~ kn2,
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ~ kn2,
    inference(flattening,[],[f46]) ).

fof(f46,negated_conjecture,
    ~ kn2,
    inference(negated_conjecture,[],[f45]) ).

fof(f45,conjecture,
    kn2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).

fof(f12640,plain,
    ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
    inference(superposition,[],[f12568,f222]) ).

fof(f222,plain,
    ! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
    inference(forward_demodulation,[],[f201,f111]) ).

fof(f201,plain,
    ! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = not(and(and(X0,X1),not(X2))),
    inference(superposition,[],[f113,f159]) ).

fof(f159,plain,
    ! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
    inference(forward_demodulation,[],[f112,f110]) ).

fof(f12568,plain,
    ! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
    inference(resolution,[],[f12492,f128]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(or(X1,X0))
      | is_a_theorem(or(X0,X1)) ),
    inference(resolution,[],[f120,f118]) ).

fof(f118,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100,f113,f101,f114,f102,f115,f103,f116,f104,f117,f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
      | ~ r3 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
    | ~ r3 ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,plain,
    ( r3
   => ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(unused_predicate_definition_removal,[],[f56]) ).

fof(f56,plain,
    ( r3
  <=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ( r3
  <=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).

fof(f117,plain,
    ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100,f113,f101,f114,f102,f115,f103,f116,f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X1,or(X0,X1)))
      | ~ r2 ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
    | ~ r2 ),
    inference(ennf_transformation,[],[f62]) ).

fof(f62,plain,
    ( r2
   => ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f55]) ).

fof(f55,plain,
    ( r2
  <=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ( r2
  <=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).

fof(f116,plain,
    ! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100,f113,f101,f114,f102,f115,f103]) ).

fof(f103,plain,
    ! [X0] :
      ( is_a_theorem(implies(or(X0,X0),X0))
      | ~ r1 ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
    | ~ r1 ),
    inference(ennf_transformation,[],[f63]) ).

fof(f63,plain,
    ( r1
   => ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(unused_predicate_definition_removal,[],[f54]) ).

fof(f54,plain,
    ( r1
  <=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ( r1
  <=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(implies(X0,X1))
      | is_a_theorem(X1)
      | ~ is_a_theorem(X0) ),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100,f113,f101,f114,f102,f115,f103,f116,f104,f117,f105,f118,f106,f119,f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f66]) ).

fof(f66,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/benchmark/theBenchmark.p',modus_ponens) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(equiv(X0,X1))
      | X0 = X1 ),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100,f113,f101,f114,f102,f115,f103,f116,f104,f117,f105,f118,f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ is_a_theorem(equiv(X0,X1))
      | ~ substitution_of_equivalents ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ is_a_theorem(equiv(X0,X1)) )
    | ~ substitution_of_equivalents ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,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/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f12492,plain,
    ! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
    inference(resolution,[],[f7331,f1165]) ).

fof(f1165,plain,
    ! [X0,X1] : is_a_theorem(or(and(not(X0),X1),implies(X1,X0))),
    inference(resolution,[],[f1113,f128]) ).

fof(f1113,plain,
    ! [X0,X1] : is_a_theorem(or(implies(X0,X1),and(not(X1),X0))),
    inference(superposition,[],[f1107,f137]) ).

fof(f137,plain,
    ! [X2,X0,X1] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2),
    inference(superposition,[],[f110,f111]) ).

fof(f1107,plain,
    ! [X0,X1] : is_a_theorem(implies(and(X0,X1),and(X1,X0))),
    inference(forward_demodulation,[],[f885,f222]) ).

fof(f885,plain,
    ! [X0,X1] : is_a_theorem(or(implies(X0,not(X1)),and(X1,X0))),
    inference(resolution,[],[f640,f128]) ).

fof(f640,plain,
    ! [X0,X1] : is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
    inference(forward_demodulation,[],[f608,f110]) ).

fof(f608,plain,
    ! [X0,X1] : is_a_theorem(or(and(X0,X1),or(not(X1),not(X0)))),
    inference(superposition,[],[f125,f166]) ).

fof(f166,plain,
    ! [X2,X0,X1] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
    inference(superposition,[],[f110,f159]) ).

fof(f125,plain,
    ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
    inference(superposition,[],[f118,f110]) ).

fof(f7331,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(or(and(X2,X0),X1))
      | is_a_theorem(or(X0,X1)) ),
    inference(forward_demodulation,[],[f7266,f166]) ).

fof(f7266,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(or(X0,X1))
      | ~ is_a_theorem(implies(implies(X2,not(X0)),X1)) ),
    inference(resolution,[],[f1062,f233]) ).

fof(f233,plain,
    ! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
    inference(superposition,[],[f124,f205]) ).

fof(f205,plain,
    ! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
    inference(superposition,[],[f113,f111]) ).

fof(f124,plain,
    ! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
    inference(superposition,[],[f117,f110]) ).

fof(f1062,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(or(X2,X0))
      | is_a_theorem(or(X2,X1))
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(resolution,[],[f319,f120]) ).

fof(f319,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(or(X0,X1),or(X0,X2)))
      | ~ is_a_theorem(implies(X1,X2)) ),
    inference(resolution,[],[f121,f120]) ).

fof(f121,plain,
    ! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))),
    inference(global_subsumption,[],[f83,f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f110,f98,f111,f99,f112,f100,f113,f101,f114,f102,f115,f103,f116,f104,f117,f105,f118,f106,f119,f107,f120,f108]) ).

fof(f108,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
      | ~ r5 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
    | ~ r5 ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,plain,
    ( r5
   => ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
    inference(unused_predicate_definition_removal,[],[f57]) ).

fof(f57,plain,
    ( r5
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
    inference(rectify,[],[f26]) ).

fof(f26,axiom,
    ( r5
  <=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : LCL500+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Apr 29 23:12:25 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (4415)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (4418)WARNING: value z3 for option sas not known
% 0.14/0.37  % (4416)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (4417)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (4419)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (4418)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)
% 0.14/0.37  % (4420)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)
% 0.14/0.37  % (4421)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)
% 0.14/0.37  % (4422)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)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [4]
% 0.22/0.43  TRYING [4]
% 0.22/0.48  TRYING [1]
% 0.22/0.48  TRYING [2]
% 0.22/0.48  TRYING [5]
% 0.22/0.48  TRYING [3]
% 0.22/0.49  TRYING [4]
% 1.31/0.54  TRYING [5]
% 1.31/0.58  TRYING [5]
% 2.52/0.71  TRYING [6]
% 2.52/0.75  TRYING [6]
% 3.72/0.87  % (4418)First to succeed.
% 3.72/0.88  % (4418)Refutation found. Thanks to Tanya!
% 3.72/0.88  % SZS status Theorem for theBenchmark
% 3.72/0.88  % SZS output start Proof for theBenchmark
% See solution above
% 3.72/0.88  % (4418)------------------------------
% 3.72/0.88  % (4418)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 3.72/0.88  % (4418)Termination reason: Refutation
% 3.72/0.88  
% 3.72/0.88  % (4418)Memory used [KB]: 5741
% 3.72/0.88  % (4418)Time elapsed: 0.502 s
% 3.72/0.88  % (4418)Instructions burned: 1227 (million)
% 3.72/0.88  % (4418)------------------------------
% 3.72/0.88  % (4418)------------------------------
% 3.72/0.88  % (4415)Success in time 0.52 s
%------------------------------------------------------------------------------