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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : LCL517+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:06:49 PM UTC 2026

% Result   : Theorem 2.75s 1.29s
% Output   : CNFRefutation 2.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  112 (  51 unt;   0 def)
%            Number of atoms       :  189 (  17 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  144 (  67   ~;  60   |;   2   &)
%                                         (   5 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   9 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :  156 (   0 sgn 155   !;   1   ?; 101   :)

% Comments : 
%------------------------------------------------------------------------------
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/Axioms/LCL006+0.ax',modus_ponens) ).

fof(f16,axiom,
    ( kn1
  <=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).

fof(f17,axiom,
    ( kn2
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).

fof(f18,axiom,
    ( kn3
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).

fof(f21,axiom,
    ( cn3
  <=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).

fof(f27,axiom,
    ( op_or
   => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).

fof(f29,axiom,
    ( op_implies_and
   => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).

fof(f31,axiom,
    ( op_equiv
   => ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).

fof(f33,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).

fof(f36,axiom,
    kn1,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).

fof(f37,axiom,
    kn2,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).

fof(f38,axiom,
    kn3,
    file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).

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

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

fof(f43,conjecture,
    cn3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).

fof(f44,negated_conjecture,
    ~ cn3,
    inference(negated_conjecture,[status(cth)],[f43]) ).

fof(f45,plain,
    ~ cn3,
    inference(flattening,[],[f44]) ).

fof(f46,plain,
    ( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
   => cn3 ),
    inference(unused_predicate_definition_removal,[],[f21]) ).

fof(f47,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,[],[f18]) ).

fof(f48,plain,
    ( kn2
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(unused_predicate_definition_removal,[],[f17]) ).

fof(f49,plain,
    ( kn1
   => ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(unused_predicate_definition_removal,[],[f16]) ).

fof(f51,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(f55,plain,
    ( ~ modus_ponens
    | ! [X0,X1] :
        ( ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0)
        | is_a_theorem(X1) ) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f56,plain,
    ( ~ modus_ponens
    | ! [X0,X1] :
        ( ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0)
        | is_a_theorem(X1) ) ),
    inference(flattening,[],[f55]) ).

fof(f58,plain,
    ( ~ kn1
    | ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f59,plain,
    ( ~ kn2
    | ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f60,plain,
    ( ~ kn3
    | ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f61,plain,
    ( ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0))
    | cn3 ),
    inference(ennf_transformation,[],[f46]) ).

fof(f62,plain,
    ( ~ op_or
    | ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f63,plain,
    ( ~ op_implies_and
    | ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f64,plain,
    ( ~ op_equiv
    | ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f65,plain,
    ( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
    | cn3 ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f61]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ~ modus_ponens
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ kn1
      | is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ kn2
      | is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f70,plain,
    ! [X2,X0,X1] :
      ( ~ kn3
      | is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f71,plain,
    ( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
    | cn3 ),
    inference(cnf_transformation,[],[f65]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ~ op_or
      | or(X0,X1) = not(and(not(X0),not(X1))) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ op_implies_and
      | implies(X0,X1) = not(and(X0,not(X1))) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ~ op_equiv
      | equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f76,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f78,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f79,plain,
    kn1,
    inference(cnf_transformation,[],[f36]) ).

fof(f80,plain,
    kn2,
    inference(cnf_transformation,[],[f37]) ).

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

fof(f83,plain,
    op_or,
    inference(cnf_transformation,[],[f40]) ).

fof(f84,plain,
    op_equiv,
    inference(cnf_transformation,[],[f42]) ).

fof(f85,plain,
    ~ cn3,
    inference(cnf_transformation,[],[f45]) ).

tcf(c_49,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(X1)
      | ~ modus_ponens
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(cnf_transformation,[],[f66]) ).

tcf(c_51,plain,
    ! [X0: $i] :
      ( is_a_theorem(implies(X0,and(X0,X0)))
      | ~ kn1 ),
    inference(cnf_transformation,[],[f68]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ kn2 ),
    inference(cnf_transformation,[],[f69]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
      | ~ kn3 ),
    inference(cnf_transformation,[],[f70]) ).

tcf(c_54,plain,
    ( cn3
    | ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
    inference(cnf_transformation,[],[f71]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i] :
      ( ( not(and(not(X0),not(X1))) = or(X0,X1) )
      | ~ op_or ),
    inference(cnf_transformation,[],[f72]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i] :
      ( ( not(and(X0,not(X1))) = implies(X0,X1) )
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f73]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i] :
      ( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
      | ~ op_equiv ),
    inference(cnf_transformation,[],[f74]) ).

tcf(c_59,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f76]) ).

tcf(c_61,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f78]) ).

tcf(c_62,plain,
    kn1,
    inference(cnf_transformation,[],[f79]) ).

tcf(c_63,plain,
    kn2,
    inference(cnf_transformation,[],[f80]) ).

tcf(c_64,plain,
    kn3,
    inference(cnf_transformation,[],[f81]) ).

tcf(c_66,plain,
    op_or,
    inference(cnf_transformation,[],[f83]) ).

tcf(c_67,plain,
    op_equiv,
    inference(cnf_transformation,[],[f84]) ).

tcf(c_68,negated_conjecture,
    ~ cn3,
    inference(cnf_transformation,[],[f85]) ).

tcf(c_76,plain,
    ! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
    inference(global_subsumption_just,[status(thm)],[c_52,c_63,c_52]) ).

tcf(c_79,plain,
    ! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
    inference(global_subsumption_just,[status(thm)],[c_51,c_62,c_51]) ).

tcf(c_82,plain,
    ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)),
    inference(global_subsumption_just,[status(thm)],[c_54,c_68,c_54]) ).

tcf(c_87,plain,
    ! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_56,c_59,c_56]) ).

tcf(c_90,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_61,c_49]) ).

tcf(c_91,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(X0)
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(renaming,[status(thm)],[c_90]) ).

tcf(c_92,plain,
    ! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_55,c_66,c_55]) ).

tcf(c_95,plain,
    ! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_57,c_67,c_57]) ).

tcf(c_98,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
    inference(global_subsumption_just,[status(thm)],[c_53,c_64,c_53]) ).

tcf(c_151,plain,
    ! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
    inference(demodulation,[status(thm)],[c_92,c_87]) ).

tcf(c_152,plain,
    ~ is_a_theorem(implies(or(sK0,sK0),sK0)),
    inference(demodulation,[status(thm)],[c_82,c_151]) ).

tcf(c_153,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
    inference(demodulation,[status(thm)],[c_98,c_151]) ).

tcf(c_347,plain,
    ! [X0: $i,X1: $i,X2: $i] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
    inference(superposition,[status(thm)],[c_87,c_151]) ).

tcf(c_358,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(X0)
      | ~ is_a_theorem(and(X0,X1)) ),
    inference(superposition,[status(thm)],[c_76,c_91]) ).

tcf(c_372,plain,
    ! [X0: $i] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
    inference(superposition,[status(thm)],[c_95,c_79]) ).

tcf(c_373,plain,
    ! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
    inference(superposition,[status(thm)],[c_95,c_76]) ).

tcf(c_380,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
    inference(superposition,[status(thm)],[c_87,c_153]) ).

tcf(c_383,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
    inference(light_normalisation,[status(thm)],[c_380,c_151]) ).

tcf(c_415,plain,
    ! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
    inference(superposition,[status(thm)],[c_151,c_373]) ).

tcf(c_435,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(or(X0,X1))
      | ~ is_a_theorem(equiv(not(X0),X1)) ),
    inference(superposition,[status(thm)],[c_415,c_91]) ).

tcf(c_465,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,not(X2)),or(X2,X0)))),
    inference(superposition,[status(thm)],[c_151,c_383]) ).

tcf(c_466,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(or(and(X1,X2),implies(X2,X0)))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(superposition,[status(thm)],[c_383,c_91]) ).

tcf(c_575,plain,
    ! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
    inference(demodulation,[status(thm)],[c_465,c_347]) ).

tcf(c_579,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(superposition,[status(thm)],[c_575,c_91]) ).

tcf(c_657,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(or(X1,X2))
      | ~ is_a_theorem(or(X2,X0))
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(superposition,[status(thm)],[c_579,c_91]) ).

tcf(c_1102,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(or(and(X1,X1),X0))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(superposition,[status(thm)],[c_79,c_657]) ).

tcf(c_1103,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(or(X1,X0))
      | ~ is_a_theorem(or(X0,and(X1,X2))) ),
    inference(superposition,[status(thm)],[c_76,c_657]) ).

tcf(c_1105,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(or(equiv(X1,X1),X0))
      | ~ is_a_theorem(or(X0,implies(X1,X1))) ),
    inference(superposition,[status(thm)],[c_372,c_657]) ).

tcf(c_1189,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(implies(implies(not(X1),X1),X0))
      | ~ is_a_theorem(or(X0,not(X1))) ),
    inference(superposition,[status(thm)],[c_347,c_1102]) ).

tcf(c_1207,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(or(X0,and(X2,X2)))
      | ~ is_a_theorem(or(and(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_1102,c_1103]) ).

tcf(c_1249,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(or(equiv(X0,X0),and(X1,X0)))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(superposition,[status(thm)],[c_466,c_1105]) ).

tcf(c_1282,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(implies(or(X1,X1),X0))
      | ~ is_a_theorem(or(X0,not(X1))) ),
    inference(demodulation,[status(thm)],[c_1189,c_151]) ).

tcf(c_1292,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(X0)
      | ~ is_a_theorem(or(X1,X1))
      | ~ is_a_theorem(or(X0,not(X1))) ),
    inference(superposition,[status(thm)],[c_1282,c_91]) ).

tcf(c_1293,plain,
    ~ is_a_theorem(or(sK0,not(sK0))),
    inference(superposition,[status(thm)],[c_1282,c_152]) ).

tcf(c_1374,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( is_a_theorem(or(X0,and(X2,X2)))
      | ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
    inference(superposition,[status(thm)],[c_347,c_1207]) ).

tcf(c_1458,plain,
    ! [X0: $i,X1: $i] :
      ( is_a_theorem(or(X1,equiv(X0,X0)))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(superposition,[status(thm)],[c_1249,c_1103]) ).

tcf(c_1692,plain,
    ! [X0: $i] : is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))),
    inference(superposition,[status(thm)],[c_372,c_1374]) ).

tcf(c_1758,plain,
    ! [X0: $i] : is_a_theorem(or(equiv(X0,X0),X0)),
    inference(superposition,[status(thm)],[c_1692,c_1103]) ).

tcf(c_1779,plain,
    ! [X0: $i] :
      ( is_a_theorem(equiv(not(X0),not(X0)))
      | ~ is_a_theorem(or(X0,X0)) ),
    inference(superposition,[status(thm)],[c_1758,c_1292]) ).

tcf(c_1919,plain,
    ! [X0: $i] :
      ( is_a_theorem(or(X0,not(X0)))
      | ~ is_a_theorem(or(X0,X0)) ),
    inference(superposition,[status(thm)],[c_1779,c_435]) ).

tcf(c_1969,plain,
    ! [X0: $i] :
      ( is_a_theorem(X0)
      | ~ is_a_theorem(or(X0,X0)) ),
    inference(superposition,[status(thm)],[c_1919,c_1292]) ).

tcf(c_2401,plain,
    ! [X0: $i] :
      ( is_a_theorem(and(X0,X0))
      | ~ is_a_theorem(or(and(X0,X0),X0)) ),
    inference(superposition,[status(thm)],[c_1102,c_1969]) ).

tcf(c_2432,plain,
    ! [X0: $i] :
      ( is_a_theorem(and(equiv(X0,X0),equiv(X0,X0)))
      | ~ is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))) ),
    inference(superposition,[status(thm)],[c_1458,c_2401]) ).

tcf(c_2441,plain,
    ! [X0: $i] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
    inference(forward_subsumption_resolution,[status(thm)],[c_2432,c_1692]) ).

tcf(c_2448,plain,
    ! [X0: $i] : is_a_theorem(equiv(X0,X0)),
    inference(superposition,[status(thm)],[c_2441,c_358]) ).

tcf(c_2460,plain,
    ! [X0: $i] : is_a_theorem(or(X0,not(X0))),
    inference(superposition,[status(thm)],[c_2448,c_435]) ).

tcf(c_2461,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_1293,c_2460]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL517+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.58  % Computer : n007.cluster.edu
% 0.10/0.58  % Model    : x86_64 x86_64
% 0.10/0.58  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58  % Memory   : 8046.5625MB
% 0.10/0.58  % OS       : Linux 6.8.0-71-generic
% 0.10/0.58  % CPULimit : 300
% 0.10/0.58  % WCLimit  : 300
% 0.10/0.58  % DateTime : Wed Sep 23 23:35:38 UTC 2026
% 0.10/0.58  % CPUTime  : 
% 0.10/0.58  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.62  Running first-order theorem proving
% 0.10/0.62  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.63  
% 0.10/0.63  % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.63  
% 0.13/0.63  % Detected problem language: tptp
% 0.13/0.64  % Proving...
% 2.75/1.29  % SZS status Started for theBenchmark.p
% 2.75/1.29  % SZS status Theorem for theBenchmark.p
% 2.75/1.29  
% 2.75/1.29  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.75/1.29  
% 2.75/1.29  % ------  iProver source info
% 2.75/1.29  
% 2.75/1.29  % git: date: 2026-07-19 20:42:38 +0200
% 2.75/1.29  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.75/1.29  % git: non_committed_changes: false
% 2.75/1.29  
% 2.75/1.29  % ------ Parsing...
% 2.75/1.29  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 2.75/1.29  
% 2.75/1.29  % ------ Preprocessing... sup_sim: 3  sf_s  rm: 10 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 2.75/1.29  
% 2.75/1.29  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 2.75/1.29  
% 2.75/1.29  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.75/1.29  % ------ Proving...
% 2.75/1.29  % ------ Problem Properties 
% 2.75/1.29  
% 2.75/1.29  % 
% 2.75/1.29  % clauses                               9
% 2.75/1.29  % conjectures                           0
% 2.75/1.29  % EPR                                   0
% 2.75/1.29  % Horn                                  9
% 2.75/1.29  % unary                                 7
% 2.75/1.29  % binary                                1
% 2.75/1.29  % lits                                  12
% 2.75/1.29  % lits eq                               4
% 2.75/1.29  % fd_pure                               0
% 2.75/1.29  % fd_pseudo                             0
% 2.75/1.29  % fd_cond                               0
% 2.75/1.29  % fd_pseudo_cond                        1
% 2.75/1.29  % AC symbols                            0
% 2.75/1.29  
% 2.75/1.29  % ------ Schedule dynamic 5 is on 
% 2.75/1.29  
% 2.75/1.29  % ------ no conjectures: strip conj schedule 
% 2.75/1.29  
% 2.75/1.29  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.75/1.29  
% 2.75/1.29  
% 2.75/1.29  % ------ 
% 2.75/1.29  % Current options:
% 2.75/1.29  % ------ 
% 2.75/1.29  
% 2.75/1.29  
% 2.75/1.29  % 
% 2.75/1.29  
% 2.75/1.29  % ------ Proving...
% 2.75/1.29  % 
% 2.75/1.29  
% 2.75/1.29  % SZS status Theorem for theBenchmark.p
% 2.75/1.29  
% 2.75/1.29  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.75/1.30  
% 2.75/1.30  
%------------------------------------------------------------------------------