TSTP Solution File: GRP776+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 : Fri May  3 02:23:39 EDT 2024

% Result   : Theorem 196.09s 26.66s
% Output   : CNFRefutation 196.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  131 (  39 unt;   0 def)
%            Number of atoms       :  258 ( 104 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  235 ( 108   ~;  96   |;  12   &)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :  141 (   7 sgn  64   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X1] :
      ( g(X1)
     => g(inv(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).

fof(f3,axiom,
    g(eh),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).

fof(f6,axiom,
    ! [X1] :
      ( g(X1)
     => product(X1,eh) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).

fof(f8,axiom,
    ! [X1] :
      ( g(X1)
     => eh = product(inv(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( h(X0)
        & h(X1) )
     => h(sum(X1,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( h(X1)
     => h(opp(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).

fof(f11,axiom,
    h(eg),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).

fof(f12,axiom,
    ! [X2,X0,X1] :
      ( ( h(X2)
        & h(X0)
        & h(X1) )
     => sum(sum(X1,X0),X2) = sum(X1,sum(X0,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).

fof(f13,axiom,
    ! [X1] :
      ( h(X1)
     => sum(eg,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).

fof(f14,axiom,
    ! [X1] :
      ( h(X1)
     => sum(X1,eg) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).

fof(f15,axiom,
    ! [X1] :
      ( h(X1)
     => eg = sum(X1,opp(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos15) ).

fof(f17,axiom,
    ! [X1] :
      ( g(X1)
     => h(f(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos17) ).

fof(f18,axiom,
    ! [X0,X1] : f(product(X1,X0)) = sum(f(X1),f(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos18) ).

fof(f19,conjecture,
    ! [X3] :
      ( ( f(inv(X3)) = opp(f(X3))
        | ~ g(X3) )
      & eg = f(eh) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f20,negated_conjecture,
    ~ ! [X3] :
        ( ( f(inv(X3)) = opp(f(X3))
          | ~ g(X3) )
        & eg = f(eh) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f21,plain,
    ! [X0] :
      ( g(X0)
     => g(inv(X0)) ),
    inference(rectify,[],[f2]) ).

fof(f24,plain,
    ! [X0] :
      ( g(X0)
     => product(X0,eh) = X0 ),
    inference(rectify,[],[f6]) ).

fof(f26,plain,
    ! [X0] :
      ( g(X0)
     => eh = product(inv(X0),X0) ),
    inference(rectify,[],[f8]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( h(X0)
        & h(X1)
        & h(X2) )
     => sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0)) ),
    inference(rectify,[],[f12]) ).

fof(f28,plain,
    ! [X0] :
      ( h(X0)
     => sum(eg,X0) = X0 ),
    inference(rectify,[],[f13]) ).

fof(f29,plain,
    ! [X0] :
      ( h(X0)
     => sum(X0,eg) = X0 ),
    inference(rectify,[],[f14]) ).

fof(f30,plain,
    ! [X0] :
      ( h(X0)
     => eg = sum(X0,opp(X0)) ),
    inference(rectify,[],[f15]) ).

fof(f32,plain,
    ! [X0] :
      ( g(X0)
     => h(f(X0)) ),
    inference(rectify,[],[f17]) ).

fof(f33,plain,
    ~ ! [X0] :
        ( ( f(inv(X0)) = opp(f(X0))
          | ~ g(X0) )
        & eg = f(eh) ),
    inference(rectify,[],[f20]) ).

fof(f36,plain,
    ! [X0] :
      ( g(inv(X0))
      | ~ g(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f40,plain,
    ! [X0] :
      ( product(X0,eh) = X0
      | ~ g(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f42,plain,
    ! [X0] :
      ( eh = product(inv(X0),X0)
      | ~ g(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( h(sum(X1,X0))
      | ~ h(X0)
      | ~ h(X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( h(sum(X1,X0))
      | ~ h(X0)
      | ~ h(X1) ),
    inference(flattening,[],[f43]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( h(opp(X0))
      | ~ h(X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
      | ~ h(X0)
      | ~ h(X1)
      | ~ h(X2) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
      | ~ h(X0)
      | ~ h(X1)
      | ~ h(X2) ),
    inference(flattening,[],[f46]) ).

fof(f48,plain,
    ! [X0] :
      ( sum(eg,X0) = X0
      | ~ h(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f49,plain,
    ! [X0] :
      ( sum(X0,eg) = X0
      | ~ h(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f50,plain,
    ! [X0] :
      ( eg = sum(X0,opp(X0))
      | ~ h(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f52,plain,
    ! [X0] :
      ( h(f(X0))
      | ~ g(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f53,plain,
    ? [X0] :
      ( ( f(inv(X0)) != opp(f(X0))
        & g(X0) )
      | eg != f(eh) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f54,plain,
    ( ? [X0] :
        ( ( f(inv(X0)) != opp(f(X0))
          & g(X0) )
        | eg != f(eh) )
   => ( ( f(inv(sK0)) != opp(f(sK0))
        & g(sK0) )
      | eg != f(eh) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ( ( f(inv(sK0)) != opp(f(sK0))
      & g(sK0) )
    | eg != f(eh) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f53,f54]) ).

fof(f57,plain,
    ! [X0] :
      ( g(inv(X0))
      | ~ g(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f58,plain,
    g(eh),
    inference(cnf_transformation,[],[f3]) ).

fof(f61,plain,
    ! [X0] :
      ( product(X0,eh) = X0
      | ~ g(X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f63,plain,
    ! [X0] :
      ( eh = product(inv(X0),X0)
      | ~ g(X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( h(sum(X1,X0))
      | ~ h(X0)
      | ~ h(X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( h(opp(X0))
      | ~ h(X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f66,plain,
    h(eg),
    inference(cnf_transformation,[],[f11]) ).

fof(f67,plain,
    ! [X2,X0,X1] :
      ( sum(sum(X2,X1),X0) = sum(X2,sum(X1,X0))
      | ~ h(X0)
      | ~ h(X1)
      | ~ h(X2) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f68,plain,
    ! [X0] :
      ( sum(eg,X0) = X0
      | ~ h(X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f69,plain,
    ! [X0] :
      ( sum(X0,eg) = X0
      | ~ h(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f70,plain,
    ! [X0] :
      ( eg = sum(X0,opp(X0))
      | ~ h(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f72,plain,
    ! [X0] :
      ( h(f(X0))
      | ~ g(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f73,plain,
    ! [X0,X1] : f(product(X1,X0)) = sum(f(X1),f(X0)),
    inference(cnf_transformation,[],[f18]) ).

fof(f74,plain,
    ( g(sK0)
    | eg != f(eh) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f75,plain,
    ( f(inv(sK0)) != opp(f(sK0))
    | eg != f(eh) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_50,plain,
    ( ~ g(X0)
    | g(inv(X0)) ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_51,plain,
    g(eh),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_54,plain,
    ( ~ g(X0)
    | product(X0,eh) = X0 ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_56,plain,
    ( ~ g(X0)
    | product(inv(X0),X0) = eh ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_57,plain,
    ( ~ h(X0)
    | ~ h(X1)
    | h(sum(X0,X1)) ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_58,plain,
    ( ~ h(X0)
    | h(opp(X1)) ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_59,plain,
    h(eg),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_60,plain,
    ( ~ h(X0)
    | ~ h(X1)
    | ~ h(X2)
    | sum(sum(X2,X0),X1) = sum(X2,sum(X0,X1)) ),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_61,plain,
    ( ~ h(X0)
    | sum(eg,X0) = X0 ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_62,plain,
    ( ~ h(X0)
    | sum(X0,eg) = X0 ),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_63,plain,
    ( ~ h(X0)
    | sum(X0,opp(X0)) = eg ),
    inference(cnf_transformation,[],[f70]) ).

cnf(c_65,plain,
    ( ~ g(X0)
    | h(f(X0)) ),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_66,plain,
    sum(f(X0),f(X1)) = f(product(X0,X1)),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_67,negated_conjecture,
    ( opp(f(sK0)) != f(inv(sK0))
    | f(eh) != eg ),
    inference(cnf_transformation,[],[f75]) ).

cnf(c_68,negated_conjecture,
    ( f(eh) != eg
    | g(sK0) ),
    inference(cnf_transformation,[],[f74]) ).

cnf(c_180,negated_conjecture,
    ( f(eh) != eg
    | g(sK0) ),
    inference(subtyping,[status(esa)],[c_68]) ).

cnf(c_181,negated_conjecture,
    ( opp(f(sK0)) != f(inv(sK0))
    | f(eh) != eg ),
    inference(subtyping,[status(esa)],[c_67]) ).

cnf(c_182,plain,
    sum(f(X0_14),f(X1_14)) = f(product(X0_14,X1_14)),
    inference(subtyping,[status(esa)],[c_66]) ).

cnf(c_183,plain,
    ( ~ g(X0_14)
    | h(f(X0_14)) ),
    inference(subtyping,[status(esa)],[c_65]) ).

cnf(c_185,plain,
    ( ~ h(X0_13)
    | sum(X0_13,opp(X0_13)) = eg ),
    inference(subtyping,[status(esa)],[c_63]) ).

cnf(c_186,plain,
    ( ~ h(X0_13)
    | sum(X0_13,eg) = X0_13 ),
    inference(subtyping,[status(esa)],[c_62]) ).

cnf(c_187,plain,
    ( ~ h(X0_13)
    | sum(eg,X0_13) = X0_13 ),
    inference(subtyping,[status(esa)],[c_61]) ).

cnf(c_188,plain,
    ( ~ h(X0_13)
    | ~ h(X1_13)
    | ~ h(X2_13)
    | sum(sum(X2_13,X0_13),X1_13) = sum(X2_13,sum(X0_13,X1_13)) ),
    inference(subtyping,[status(esa)],[c_60]) ).

cnf(c_189,plain,
    h(eg),
    inference(subtyping,[status(esa)],[c_59]) ).

cnf(c_190,plain,
    ( ~ h(X0_13)
    | h(opp(X1_13)) ),
    inference(subtyping,[status(esa)],[c_58]) ).

cnf(c_191,plain,
    ( ~ h(X0_13)
    | ~ h(X1_13)
    | h(sum(X0_13,X1_13)) ),
    inference(subtyping,[status(esa)],[c_57]) ).

cnf(c_192,plain,
    ( ~ g(X0_14)
    | product(inv(X0_14),X0_14) = eh ),
    inference(subtyping,[status(esa)],[c_56]) ).

cnf(c_194,plain,
    ( ~ g(X0_14)
    | product(X0_14,eh) = X0_14 ),
    inference(subtyping,[status(esa)],[c_54]) ).

cnf(c_197,plain,
    g(eh),
    inference(subtyping,[status(esa)],[c_51]) ).

cnf(c_198,plain,
    ( ~ g(X0_14)
    | g(inv(X0_14)) ),
    inference(subtyping,[status(esa)],[c_50]) ).

cnf(c_200,plain,
    ( h(opp(X0_13))
    | ~ sP0_iProver_def ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_190]) ).

cnf(c_201,plain,
    ( ~ h(X0_13)
    | ~ sP1_iProver_def ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP1_iProver_def])],[c_190]) ).

cnf(c_202,plain,
    ( sP0_iProver_def
    | sP1_iProver_def ),
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_190]) ).

cnf(c_526,plain,
    ~ sP1_iProver_def,
    inference(superposition,[status(thm)],[c_189,c_201]) ).

cnf(c_528,plain,
    sP0_iProver_def,
    inference(backward_subsumption_resolution,[status(thm)],[c_202,c_526]) ).

cnf(c_529,plain,
    h(opp(X0_13)),
    inference(backward_subsumption_resolution,[status(thm)],[c_200,c_528]) ).

cnf(c_533,plain,
    ( ~ g(X0_14)
    | sum(f(X0_14),eg) = f(X0_14) ),
    inference(superposition,[status(thm)],[c_183,c_186]) ).

cnf(c_540,plain,
    sum(eg,opp(X0_13)) = opp(X0_13),
    inference(superposition,[status(thm)],[c_529,c_187]) ).

cnf(c_544,plain,
    product(eh,eh) = eh,
    inference(superposition,[status(thm)],[c_197,c_194]) ).

cnf(c_566,plain,
    ( ~ g(X0_14)
    | sum(f(X0_14),opp(f(X0_14))) = eg ),
    inference(superposition,[status(thm)],[c_183,c_185]) ).

cnf(c_567,plain,
    sum(opp(X0_13),opp(opp(X0_13))) = eg,
    inference(superposition,[status(thm)],[c_529,c_185]) ).

cnf(c_580,plain,
    ( ~ h(X0_13)
    | ~ h(X1_13)
    | sum(sum(X0_13,X1_13),opp(sum(X0_13,X1_13))) = eg ),
    inference(superposition,[status(thm)],[c_191,c_185]) ).

cnf(c_623,plain,
    sum(f(eh),eg) = f(eh),
    inference(superposition,[status(thm)],[c_197,c_533]) ).

cnf(c_624,plain,
    ( ~ g(X0_14)
    | sum(f(inv(X0_14)),eg) = f(inv(X0_14)) ),
    inference(superposition,[status(thm)],[c_198,c_533]) ).

cnf(c_639,plain,
    ( ~ g(X0_14)
    | ~ h(X0_13)
    | ~ h(X1_13)
    | sum(sum(X1_13,f(X0_14)),X0_13) = sum(X1_13,sum(f(X0_14),X0_13)) ),
    inference(superposition,[status(thm)],[c_183,c_188]) ).

cnf(c_641,plain,
    ( ~ h(X0_13)
    | ~ h(X1_13)
    | sum(sum(X1_13,opp(X2_13)),X0_13) = sum(X1_13,sum(opp(X2_13),X0_13)) ),
    inference(superposition,[status(thm)],[c_529,c_188]) ).

cnf(c_758,plain,
    sum(f(eh),opp(f(eh))) = eg,
    inference(superposition,[status(thm)],[c_197,c_566]) ).

cnf(c_1215,plain,
    ( ~ g(X0_14)
    | ~ h(X0_13)
    | sum(sum(f(X0_14),X0_13),opp(sum(f(X0_14),X0_13))) = eg ),
    inference(superposition,[status(thm)],[c_183,c_580]) ).

cnf(c_2436,plain,
    ( ~ h(X0_13)
    | sum(sum(f(eh),X0_13),opp(sum(f(eh),X0_13))) = eg ),
    inference(superposition,[status(thm)],[c_197,c_1215]) ).

cnf(c_2447,plain,
    sum(sum(f(eh),opp(X0_13)),opp(sum(f(eh),opp(X0_13)))) = eg,
    inference(superposition,[status(thm)],[c_529,c_2436]) ).

cnf(c_2710,plain,
    ( ~ h(X0_13)
    | sum(sum(X0_13,opp(X1_13)),opp(X2_13)) = sum(X0_13,sum(opp(X1_13),opp(X2_13))) ),
    inference(superposition,[status(thm)],[c_529,c_641]) ).

cnf(c_2766,plain,
    ( ~ g(X0_14)
    | sum(sum(f(X0_14),opp(X0_13)),opp(X1_13)) = sum(f(X0_14),sum(opp(X0_13),opp(X1_13))) ),
    inference(superposition,[status(thm)],[c_183,c_2710]) ).

cnf(c_10453,plain,
    sum(sum(f(eh),opp(X0_13)),opp(X1_13)) = sum(f(eh),sum(opp(X0_13),opp(X1_13))),
    inference(superposition,[status(thm)],[c_197,c_2766]) ).

cnf(c_10456,plain,
    sum(f(eh),sum(opp(X0_13),opp(sum(f(eh),opp(X0_13))))) = eg,
    inference(demodulation,[status(thm)],[c_2447,c_10453]) ).

cnf(c_10509,plain,
    sum(f(eh),sum(opp(f(eh)),opp(X0_13))) = sum(eg,opp(X0_13)),
    inference(superposition,[status(thm)],[c_758,c_10453]) ).

cnf(c_10523,plain,
    sum(f(eh),sum(opp(f(eh)),opp(X0_13))) = opp(X0_13),
    inference(demodulation,[status(thm)],[c_10509,c_540]) ).

cnf(c_11387,plain,
    sum(f(eh),eg) = opp(opp(f(eh))),
    inference(superposition,[status(thm)],[c_567,c_10523]) ).

cnf(c_11402,plain,
    opp(opp(f(eh))) = f(eh),
    inference(demodulation,[status(thm)],[c_11387,c_623]) ).

cnf(c_11583,plain,
    sum(f(eh),sum(f(eh),opp(sum(f(eh),f(eh))))) = eg,
    inference(superposition,[status(thm)],[c_11402,c_10456]) ).

cnf(c_11719,plain,
    f(eh) = eg,
    inference(demodulation,[status(thm)],[c_11583,c_182,c_544,c_623,c_758]) ).

cnf(c_11758,plain,
    ( opp(f(sK0)) != f(inv(sK0))
    | eg != eg ),
    inference(demodulation,[status(thm)],[c_181,c_11719]) ).

cnf(c_11759,plain,
    ( eg != eg
    | g(sK0) ),
    inference(demodulation,[status(thm)],[c_180,c_11719]) ).

cnf(c_11760,plain,
    g(sK0),
    inference(equality_resolution_simp,[status(thm)],[c_11759]) ).

cnf(c_11761,plain,
    opp(f(sK0)) != f(inv(sK0)),
    inference(equality_resolution_simp,[status(thm)],[c_11758]) ).

cnf(c_12238,plain,
    sum(f(inv(sK0)),eg) = f(inv(sK0)),
    inference(superposition,[status(thm)],[c_11760,c_624]) ).

cnf(c_12241,plain,
    sum(f(sK0),opp(f(sK0))) = eg,
    inference(superposition,[status(thm)],[c_11760,c_566]) ).

cnf(c_12250,plain,
    product(inv(sK0),sK0) = eh,
    inference(superposition,[status(thm)],[c_11760,c_192]) ).

cnf(c_90813,plain,
    ( ~ h(X0_13)
    | ~ h(X1_13)
    | sum(sum(X1_13,f(sK0)),X0_13) = sum(X1_13,sum(f(sK0),X0_13)) ),
    inference(superposition,[status(thm)],[c_11760,c_639]) ).

cnf(c_94098,plain,
    ( ~ h(X0_13)
    | sum(sum(X0_13,f(sK0)),opp(X1_13)) = sum(X0_13,sum(f(sK0),opp(X1_13))) ),
    inference(superposition,[status(thm)],[c_529,c_90813]) ).

cnf(c_94214,plain,
    ( ~ g(X0_14)
    | sum(sum(f(X0_14),f(sK0)),opp(X0_13)) = sum(f(X0_14),sum(f(sK0),opp(X0_13))) ),
    inference(superposition,[status(thm)],[c_183,c_94098]) ).

cnf(c_94225,plain,
    ( ~ g(X0_14)
    | sum(f(X0_14),sum(f(sK0),opp(X0_13))) = sum(f(product(X0_14,sK0)),opp(X0_13)) ),
    inference(demodulation,[status(thm)],[c_94214,c_182]) ).

cnf(c_94545,plain,
    ( ~ g(X0_14)
    | sum(f(inv(X0_14)),sum(f(sK0),opp(X0_13))) = sum(f(product(inv(X0_14),sK0)),opp(X0_13)) ),
    inference(superposition,[status(thm)],[c_198,c_94225]) ).

cnf(c_95540,plain,
    sum(f(inv(sK0)),sum(f(sK0),opp(X0_13))) = sum(f(product(inv(sK0),sK0)),opp(X0_13)),
    inference(superposition,[status(thm)],[c_11760,c_94545]) ).

cnf(c_95549,plain,
    sum(f(inv(sK0)),sum(f(sK0),opp(X0_13))) = opp(X0_13),
    inference(demodulation,[status(thm)],[c_95540,c_540,c_11719,c_12250]) ).

cnf(c_95855,plain,
    sum(f(inv(sK0)),eg) = opp(f(sK0)),
    inference(superposition,[status(thm)],[c_12241,c_95549]) ).

cnf(c_95863,plain,
    opp(f(sK0)) = f(inv(sK0)),
    inference(demodulation,[status(thm)],[c_95855,c_12238]) ).

cnf(c_95864,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_95863,c_11761]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.06  % Problem  : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% 0.01/0.07  % Command  : run_iprover %s %d THM
% 0.07/0.25  % Computer : n018.cluster.edu
% 0.07/0.25  % Model    : x86_64 x86_64
% 0.07/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25  % Memory   : 8042.1875MB
% 0.07/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25  % CPULimit : 300
% 0.07/0.25  % WCLimit  : 300
% 0.07/0.25  % DateTime : Thu May  2 23:55:01 EDT 2024
% 0.07/0.25  % CPUTime  : 
% 0.10/0.32  Running first-order theorem proving
% 0.10/0.32  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 41.55/6.61  % SZS status Started for theBenchmark.p
% 41.55/6.61  ERROR - "ProverProcess:heur/379306:2.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!97 (|16777216|) Bool) supplied sort is |16777230|")
% 41.55/6.61  Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!97 (|16777216|) Bool) supplied sort is |16777230|")
% 41.55/6.61  ERROR - cmd was:  ulimit -v 4096000; ./res/iproveropt_static_z3 --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground false --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;ACNormalisation]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;Demod;LightNorm;ACNormalisation]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[]" --sup_input_bw "[SubsumptionRes]" --sup_input_fw "[SMTSubs;]" --sup_input_triv "[]" --sup_iter_deepening 1 --sup_passive_queue_type priority_queues --sup_passive_queues "[[+min_def_symb;-score;+epr];[-next_state;-conj_dist;+conj_symb]]" --sup_passive_queues_freq "[3;512]" --sup_prop_simpl_given false --sup_prop_simpl_new true --sup_restarts_mult 16 --sup_score sim_d_gen --sup_share_max_num_cl 320 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering arity_rev --sup_to_prop_solver none --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --proof_out true --sat_out_model pos  --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 2.00" --time_out_real 2.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_sdksnif9/mmr282d4 2>> /export/starexec/sandbox2/tmp/iprover_out_sdksnif9/mmr282d4_error
% 196.09/26.66  % SZS status Theorem for theBenchmark.p
% 196.09/26.66  
% 196.09/26.66  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 196.09/26.66  
% 196.09/26.66  ------  iProver source info
% 196.09/26.66  
% 196.09/26.66  git: date: 2024-05-02 19:28:25 +0000
% 196.09/26.66  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 196.09/26.66  git: non_committed_changes: false
% 196.09/26.66  
% 196.09/26.66  ------ Parsing...
% 196.09/26.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 196.09/26.66  
% 196.09/26.66  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 196.09/26.66  
% 196.09/26.66  ------ Preprocessing... gs_s  sp: 2 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 196.09/26.66  
% 196.09/26.66  ------ Preprocessing... sf_s  rm: 3 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 196.09/26.66  ------ Proving...
% 196.09/26.66  ------ Problem Properties 
% 196.09/26.66  
% 196.09/26.66  
% 196.09/26.66  clauses                                 22
% 196.09/26.66  conjectures                             2
% 196.09/26.66  EPR                                     4
% 196.09/26.66  Horn                                    21
% 196.09/26.66  unary                                   3
% 196.09/26.66  binary                                  15
% 196.09/26.66  lits                                    47
% 196.09/26.66  lits eq                                 14
% 196.09/26.66  fd_pure                                 0
% 196.09/26.66  fd_pseudo                               0
% 196.09/26.66  fd_cond                                 0
% 196.09/26.66  fd_pseudo_cond                          0
% 196.09/26.66  AC symbols                              0
% 196.09/26.66  
% 196.09/26.66  ------ Input Options Time Limit: Unbounded
% 196.09/26.66  
% 196.09/26.66  
% 196.09/26.66  ------ 
% 196.09/26.66  Current options:
% 196.09/26.66  ------ 
% 196.09/26.66  
% 196.09/26.66  
% 196.09/26.66  
% 196.09/26.66  
% 196.09/26.66  ------ Proving...
% 196.09/26.66  
% 196.09/26.66  
% 196.09/26.66  % SZS status Theorem for theBenchmark.p
% 196.09/26.66  
% 196.09/26.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 196.09/26.66  
% 196.09/26.67  
%------------------------------------------------------------------------------