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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : COM132+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n008.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 01:04:28 PM UTC 2026

% Result   : Theorem 74.15s 11.21s
% Output   : CNFRefutation 74.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   70 (  18 unt;   0 def)
%            Number of atoms       :  228 (  90 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  272 ( 114   ~; 113   |;  32   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   8 con; 0-3 aty)
%            Number of variables   :  275 (   0 sgn 261   !;  14   ?;  51   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( ( X1 = vapp(X2,X4)
        & X0 = X3 )
     => ( ( visFreeVar(X0,X1)
         => ( visFreeVar(X3,X4)
            | visFreeVar(X3,X2) ) )
        & ( ( visFreeVar(X3,X4)
            | visFreeVar(X3,X2) )
         => visFreeVar(X0,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar2) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( vgensym(X1) = X0
     => ~ visFreeVar(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','gensym-is-fresh') ).

fof(f33,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
      ( ( X2 = vabs(X7,X6,X9)
        & X1 = X5
        & X0 = X4 )
     => ( ( X8 = vgensym(vapp(vapp(X5,X9),vvar(X4)))
          & visFreeVar(X7,X5)
          & X4 != X7 )
       => ( X3 = vsubst(X0,X1,X2)
         => X3 = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',subst4) ).

fof(f58,axiom,
    ! [X0,X1,X2,X3] :
      ( ~ visFreeVar(X2,X3)
     => valphaEquivalent(vabs(X1,X0,X3),vabs(X2,X0,vsubst(X1,vvar(X2),X3))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COM001+1.ax','alpha-equiv-subst-abs') ).

fof(f59,axiom,
    ! [X0,X1,X2,X3] :
      ( ( valphaEquivalent(X0,X2)
        & vtcheck(X1,X0,X3) )
     => vtcheck(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/COM001+1.ax','alpha-equiv-typing') ).

fof(f64,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
        & vtcheck(X1,X3,X0)
        & ~ visFreeVar(X4,X3)
        & X2 != X4 )
     => vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-2-gen') ).

fof(f65,axiom,
    ! [X0,X1,X2,X3] :
      ( X3 = vgensym(vapp(vapp(X0,X1),vvar(X2)))
     => X2 != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','fresh-unequal-var-3') ).

fof(f67,conjecture,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
        & vtcheck(X1,X3,X0)
        & visFreeVar(X4,X3)
        & X2 != X4 )
     => vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-3') ).

fof(f68,negated_conjecture,
    ~ ! [X0,X1,X2,X3,X4,X5,X6] :
        ( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
          & vtcheck(X1,X3,X0)
          & visFreeVar(X4,X3)
          & X2 != X4 )
       => vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
    inference(negated_conjecture,[status(cth)],[f67]) ).

fof(f88,plain,
    ! [X0,X1,X2,X3,X4] :
      ( vapp(X2,X4) != X1
      | X0 != X3
      | ( ( ~ visFreeVar(X0,X1)
          | visFreeVar(X3,X4)
          | visFreeVar(X3,X2) )
        & ( ( ~ visFreeVar(X3,X4)
            & ~ visFreeVar(X3,X2) )
          | visFreeVar(X0,X1) ) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f89,plain,
    ! [X0,X1,X2,X3,X4] :
      ( vapp(X2,X4) != X1
      | X0 != X3
      | ( ( ~ visFreeVar(X0,X1)
          | visFreeVar(X3,X4)
          | visFreeVar(X3,X2) )
        & ( ( ~ visFreeVar(X3,X4)
            & ~ visFreeVar(X3,X2) )
          | visFreeVar(X0,X1) ) ) ),
    inference(flattening,[],[f88]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( vgensym(X1) != X0
      | ~ visFreeVar(X0,X1) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f118,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
      ( vabs(X7,X6,X9) != X2
      | X1 != X5
      | X0 != X4
      | vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
      | ~ visFreeVar(X7,X5)
      | X4 = X7
      | vsubst(X0,X1,X2) != X3
      | X3 = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f119,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
      ( vabs(X7,X6,X9) != X2
      | X1 != X5
      | X0 != X4
      | vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
      | ~ visFreeVar(X7,X5)
      | X4 = X7
      | vsubst(X0,X1,X2) != X3
      | X3 = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) ),
    inference(flattening,[],[f118]) ).

fof(f156,plain,
    ! [X0,X1,X2,X3] :
      ( visFreeVar(X2,X3)
      | valphaEquivalent(vabs(X1,X0,X3),vabs(X2,X0,vsubst(X1,vvar(X2),X3))) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f157,plain,
    ! [X0,X1,X2,X3] :
      ( ~ valphaEquivalent(X0,X2)
      | ~ vtcheck(X1,X0,X3)
      | vtcheck(X1,X2,X3) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f158,plain,
    ! [X0,X1,X2,X3] :
      ( ~ valphaEquivalent(X0,X2)
      | ~ vtcheck(X1,X0,X3)
      | vtcheck(X1,X2,X3) ),
    inference(flattening,[],[f157]) ).

fof(f167,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
      | ~ vtcheck(X1,X3,X0)
      | visFreeVar(X4,X3)
      | X2 = X4
      | vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f168,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
      | ~ vtcheck(X1,X3,X0)
      | visFreeVar(X4,X3)
      | X2 = X4
      | vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
    inference(flattening,[],[f167]) ).

fof(f169,plain,
    ! [X0,X1,X2,X3] :
      ( vgensym(vapp(vapp(X0,X1),vvar(X2))) != X3
      | X2 != X3 ),
    inference(ennf_transformation,[],[f65]) ).

fof(f171,plain,
    ? [X0,X1,X2,X3,X4,X5,X6] :
      ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
      & vtcheck(X1,X3,X0)
      & visFreeVar(X4,X3)
      & X2 != X4
      & ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f172,plain,
    ? [X0,X1,X2,X3,X4,X5,X6] :
      ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
      & vtcheck(X1,X3,X0)
      & visFreeVar(X4,X3)
      & X2 != X4
      & ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
    inference(flattening,[],[f171]) ).

fof(f235,plain,
    ( vtcheck(vbind(sK89,sK87,sK88),vabs(sK91,sK92,veabs),sK93)
    & vtcheck(sK88,sK90,sK87)
    & visFreeVar(sK91,sK90)
    & sK89 != sK91
    & ~ vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88,sK89,sK90,sK91,sK92,sK93]),skolemize(X0,sK87),skolemize(X1,sK88),skolemize(X2,sK89),skolemize(X3,sK90),skolemize(X4,sK91),skolemize(X5,sK92),skolemize(X6,sK93)],[f172]) ).

fof(f257,plain,
    ! [X2,X3,X0,X1,X4] :
      ( vapp(X2,X4) != X1
      | X0 != X3
      | ~ visFreeVar(X3,X4)
      | visFreeVar(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f258,plain,
    ! [X2,X3,X0,X1,X4] :
      ( vapp(X2,X4) != X1
      | X0 != X3
      | ~ visFreeVar(X3,X2)
      | visFreeVar(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f288,plain,
    ! [X0,X1] :
      ( vgensym(X1) != X0
      | ~ visFreeVar(X0,X1) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f293,plain,
    ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
      ( vabs(X7,X6,X9) != X2
      | X1 != X5
      | X0 != X4
      | vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
      | ~ visFreeVar(X7,X5)
      | X4 = X7
      | vsubst(X0,X1,X2) != X3
      | vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X3 ),
    inference(cnf_transformation,[],[f119]) ).

fof(f387,plain,
    ! [X2,X3,X0,X1] :
      ( visFreeVar(X2,X3)
      | valphaEquivalent(vabs(X1,X0,X3),vabs(X2,X0,vsubst(X1,vvar(X2),X3))) ),
    inference(cnf_transformation,[],[f156]) ).

fof(f388,plain,
    ! [X2,X3,X0,X1] :
      ( ~ valphaEquivalent(X0,X2)
      | ~ vtcheck(X1,X0,X3)
      | vtcheck(X1,X2,X3) ),
    inference(cnf_transformation,[],[f158]) ).

fof(f393,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
      | ~ vtcheck(X1,X3,X0)
      | visFreeVar(X4,X3)
      | X2 = X4
      | vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
    inference(cnf_transformation,[],[f168]) ).

fof(f394,plain,
    ! [X2,X3,X0,X1] :
      ( vgensym(vapp(vapp(X0,X1),vvar(X2))) != X3
      | X2 != X3 ),
    inference(cnf_transformation,[],[f169]) ).

fof(f396,plain,
    vtcheck(vbind(sK89,sK87,sK88),vabs(sK91,sK92,veabs),sK93),
    inference(cnf_transformation,[],[f235]) ).

fof(f397,plain,
    vtcheck(sK88,sK90,sK87),
    inference(cnf_transformation,[],[f235]) ).

fof(f398,plain,
    visFreeVar(sK91,sK90),
    inference(cnf_transformation,[],[f235]) ).

fof(f399,plain,
    sK89 != sK91,
    inference(cnf_transformation,[],[f235]) ).

fof(f400,plain,
    ~ vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93),
    inference(cnf_transformation,[],[f235]) ).

fof(f422,plain,
    ! [X2,X3,X1,X4] :
      ( vapp(X2,X4) != X1
      | ~ visFreeVar(X3,X2)
      | visFreeVar(X3,X1) ),
    inference(equality_resolution,[],[f258]) ).

fof(f423,plain,
    ! [X2,X3,X4] :
      ( ~ visFreeVar(X3,X2)
      | visFreeVar(X3,vapp(X2,X4)) ),
    inference(equality_resolution,[],[f422]) ).

fof(f424,plain,
    ! [X2,X3,X1,X4] :
      ( vapp(X2,X4) != X1
      | ~ visFreeVar(X3,X4)
      | visFreeVar(X3,X1) ),
    inference(equality_resolution,[],[f257]) ).

fof(f425,plain,
    ! [X2,X3,X4] :
      ( ~ visFreeVar(X3,X4)
      | visFreeVar(X3,vapp(X2,X4)) ),
    inference(equality_resolution,[],[f424]) ).

fof(f450,plain,
    ! [X1] : ~ visFreeVar(vgensym(X1),X1),
    inference(equality_resolution,[],[f288]) ).

fof(f469,plain,
    ! [X2,X0,X1,X8,X6,X9,X7,X4,X5] :
      ( vabs(X7,X6,X9) != X2
      | X1 != X5
      | X0 != X4
      | vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
      | ~ visFreeVar(X7,X5)
      | X4 = X7
      | vsubst(X0,X1,X2) = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) ),
    inference(equality_resolution,[],[f293]) ).

fof(f470,plain,
    ! [X2,X0,X1,X6,X9,X7,X4,X5] :
      ( vabs(X7,X6,X9) != X2
      | X1 != X5
      | X0 != X4
      | ~ visFreeVar(X7,X5)
      | X4 = X7
      | vsubst(X0,X1,X2) = vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) ),
    inference(equality_resolution,[],[f469]) ).

fof(f471,plain,
    ! [X2,X1,X6,X9,X7,X4,X5] :
      ( vabs(X7,X6,X9) != X2
      | X1 != X5
      | ~ visFreeVar(X7,X5)
      | X4 = X7
      | vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X1,X2) ),
    inference(equality_resolution,[],[f470]) ).

fof(f472,plain,
    ! [X2,X6,X9,X7,X4,X5] :
      ( vabs(X7,X6,X9) != X2
      | ~ visFreeVar(X7,X5)
      | X4 = X7
      | vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,X2) ),
    inference(equality_resolution,[],[f471]) ).

fof(f473,plain,
    ! [X6,X9,X7,X4,X5] :
      ( ~ visFreeVar(X7,X5)
      | X4 = X7
      | vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,vabs(X7,X6,X9)) ),
    inference(equality_resolution,[],[f472]) ).

fof(f512,plain,
    ! [X3,X0,X1] : vgensym(vapp(vapp(X0,X1),vvar(X3))) != X3,
    inference(equality_resolution,[],[f394]) ).

tcf(c_66,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( visFreeVar(X0,vapp(X1,X2))
      | ~ visFreeVar(X0,X1) ),
    inference(cnf_transformation,[],[f423]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( visFreeVar(X0,vapp(X2,X1))
      | ~ visFreeVar(X0,X1) ),
    inference(cnf_transformation,[],[f425]) ).

tcf(c_94,plain,
    ! [X0: $i] : ~ visFreeVar(vgensym(X0),X0),
    inference(cnf_transformation,[],[f450]) ).

tcf(c_99,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( X0 = X2 )
      | ( vsubst(X2,X1,vabs(vgensym(vapp(vapp(X1,X3),vvar(X2))),X4,vsubst(X0,vvar(vgensym(vapp(vapp(X1,X3),vvar(X2)))),X3))) = vsubst(X2,X1,vabs(X0,X4,X3)) )
      | ~ visFreeVar(X0,X1) ),
    inference(cnf_transformation,[],[f473]) ).

tcf(c_190,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( visFreeVar(X3,X2)
      | valphaEquivalent(vabs(X0,X1,X2),vabs(X3,X1,vsubst(X0,vvar(X3),X2))) ),
    inference(cnf_transformation,[],[f387]) ).

tcf(c_191,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( vtcheck(X0,X3,X2)
      | ~ valphaEquivalent(X1,X3)
      | ~ vtcheck(X0,X1,X2) ),
    inference(cnf_transformation,[],[f388]) ).

tcf(c_196,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( visFreeVar(X3,X7)
      | vtcheck(X2,vsubst(X0,X7,vabs(X3,X4,X5)),X6)
      | ( X0 = X3 )
      | ~ vtcheck(X2,X7,X1)
      | ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,X5),X6) ),
    inference(cnf_transformation,[],[f393]) ).

tcf(c_197,plain,
    ! [X0: $i,X1: $i,X2: $i] : vgensym(vapp(vapp(X0,X1),vvar(X2))) != X2,
    inference(cnf_transformation,[],[f512]) ).

tcf(c_199,negated_conjecture,
    ~ vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93),
    inference(cnf_transformation,[],[f400]) ).

tcf(c_200,negated_conjecture,
    sK89 != sK91,
    inference(cnf_transformation,[],[f399]) ).

tcf(c_201,negated_conjecture,
    visFreeVar(sK91,sK90),
    inference(cnf_transformation,[],[f398]) ).

tcf(c_202,negated_conjecture,
    vtcheck(sK88,sK90,sK87),
    inference(cnf_transformation,[],[f397]) ).

tcf(c_203,negated_conjecture,
    vtcheck(vbind(sK89,sK87,sK88),vabs(sK91,sK92,veabs),sK93),
    inference(cnf_transformation,[],[f396]) ).

tcf(c_26392,plain,
    ! [X0: $i,X1: $i] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0),
    inference(superposition,[status(thm)],[c_66,c_94]) ).

tcf(c_26393,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0),
    inference(superposition,[status(thm)],[c_66,c_26392]) ).

tcf(c_26397,plain,
    ! [X0: $i,X1: $i,X2: $i] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1),
    inference(superposition,[status(thm)],[c_67,c_26392]) ).

tcf(c_26515,plain,
    ! [X0: $i] :
      ( vtcheck(vbind(sK89,sK87,sK88),X0,sK93)
      | ~ valphaEquivalent(vabs(sK91,sK92,veabs),X0) ),
    inference(superposition,[status(thm)],[c_203,c_191]) ).

tcf(c_28277,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( visFreeVar(X0,X3)
      | vtcheck(sK88,vsubst(sK89,X3,vabs(X0,X1,X2)),sK93)
      | ( X0 = sK89 )
      | ~ vtcheck(sK88,X3,sK87)
      | ~ valphaEquivalent(vabs(sK91,sK92,veabs),vabs(X0,X1,X2)) ),
    inference(superposition,[status(thm)],[c_26515,c_196]) ).

tcf(c_28513,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = sK91 )
      | ( vsubst(X0,sK90,vabs(vgensym(vapp(vapp(sK90,X1),vvar(X0))),X2,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X1),vvar(X0)))),X1))) = vsubst(X0,sK90,vabs(sK91,X2,X1)) ) ),
    inference(superposition,[status(thm)],[c_201,c_99]) ).

tcf(c_28615,plain,
    ! [X0: $i,X1: $i] :
      ( visFreeVar(vgensym(vapp(vapp(sK90,X0),vvar(sK89))),sK90)
      | vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,X1,X0)),sK93)
      | ( sK89 = sK91 )
      | ( vgensym(vapp(vapp(sK90,X0),vvar(sK89))) = sK89 )
      | ~ vtcheck(sK88,sK90,sK87)
      | ~ valphaEquivalent(vabs(sK91,sK92,veabs),vabs(vgensym(vapp(vapp(sK90,X0),vvar(sK89))),X1,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X0),vvar(sK89)))),X0))) ),
    inference(superposition,[status(thm)],[c_28513,c_28277]) ).

tcf(c_28616,plain,
    ! [X0: $i,X1: $i] :
      ( vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,X1,X0)),sK93)
      | ~ valphaEquivalent(vabs(sK91,sK92,veabs),vabs(vgensym(vapp(vapp(sK90,X0),vvar(sK89))),X1,vsubst(sK91,vvar(vgensym(vapp(vapp(sK90,X0),vvar(sK89)))),X0))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28615,c_26393,c_200,c_197,c_202]) ).

tcf(c_28640,plain,
    ( visFreeVar(vgensym(vapp(vapp(sK90,veabs),vvar(sK89))),veabs)
    | vtcheck(sK88,vsubst(sK89,sK90,vabs(sK91,sK92,veabs)),sK93) ),
    inference(superposition,[status(thm)],[c_190,c_28616]) ).

tcf(c_28644,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_28640,c_26397,c_199]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : COM132+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.07  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.20/0.45  % Computer : n008.cluster.edu
% 0.20/0.45  % Model    : x86_64 x86_64
% 0.20/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45  % Memory   : 8046.5625MB
% 0.20/0.45  % OS       : Linux 6.8.0-71-generic
% 0.20/0.45  % CPULimit : 300
% 0.20/0.45  % WCLimit  : 300
% 0.20/0.45  % DateTime : Fri Sep 25 07:55:12 UTC 2026
% 0.20/0.45  % CPUTime  : 
% 0.20/0.45  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.50  Running first-order theorem proving
% 0.23/0.50  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.52  
% 0.23/0.52  % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.52  
% 0.23/0.52  % Detected problem language: tptp
% 0.23/0.53  % Proving...
% 74.15/11.21  % SZS status Started for theBenchmark.p
% 74.15/11.21  % SZS status Theorem for theBenchmark.p
% 74.15/11.21  
% 74.15/11.21  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 74.15/11.21  
% 74.15/11.21  % ------  iProver source info
% 74.15/11.21  
% 74.15/11.21  % git: date: 2026-07-19 20:42:38 +0200
% 74.15/11.21  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 74.15/11.21  % git: non_committed_changes: false
% 74.15/11.21  
% 74.15/11.21  % ------ Parsing...
% 74.15/11.21  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 74.15/11.21  
% 74.15/11.21  % ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 74.15/11.21  
% 74.15/11.21  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 74.15/11.21  
% 74.15/11.21  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 74.15/11.21  % ------ Proving...
% 74.15/11.21  % ------ Problem Properties 
% 74.15/11.21  
% 74.15/11.21  % 
% 74.15/11.21  % clauses                               151
% 74.15/11.21  % conjectures                           5
% 74.15/11.21  % EPR                                   11
% 74.15/11.21  % Horn                                  121
% 74.15/11.21  % unary                                 31
% 74.15/11.21  % binary                                88
% 74.15/11.21  % lits                                  328
% 74.15/11.21  % lits eq                               136
% 74.15/11.21  % fd_pure                               0
% 74.15/11.21  % fd_pseudo                             0
% 74.15/11.21  % fd_cond                               3
% 74.15/11.21  % fd_pseudo_cond                        21
% 74.15/11.21  % AC symbols                            0
% 74.15/11.21  
% 74.15/11.21  % ------ Input Options Time Limit: Unbounded
% 74.15/11.21  
% 74.15/11.21  
% 74.15/11.21  % ------ 
% 74.15/11.21  % Current options:
% 74.15/11.21  % ------ 
% 74.15/11.21  
% 74.15/11.21  
% 74.15/11.21  % 
% 74.15/11.21  
% 74.15/11.21  % ------ Proving...
% 74.15/11.21  % 
% 74.15/11.21  
% 74.15/11.21  % SZS status Theorem for theBenchmark.p
% 74.15/11.21  
% 74.15/11.21  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 74.15/11.22  
% 74.15/11.22  
%------------------------------------------------------------------------------