TSTP Solution File: SWW246+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW246+1 : TPTP v8.1.2. Released v5.2.0.
% 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 17:29:16 EDT 2024

% Result   : ContradictoryAxioms 1.58s 0.69s
% Output   : Refutation 1.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   25 (   6 unt;   0 def)
%            Number of atoms       :   61 (  35 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   64 (  28   ~;  22   |;   4   &)
%                                         (   5 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :   56 (  52   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9364,plain,
    $false,
    inference(resolution,[],[f9363,f3677]) ).

fof(f3677,plain,
    class_Rings_Oidom(t_a),
    inference(cnf_transformation,[],[f1200]) ).

fof(f1200,axiom,
    class_Rings_Oidom(t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

fof(f9363,plain,
    ~ class_Rings_Oidom(t_a),
    inference(resolution,[],[f9349,f3785]) ).

fof(f3785,plain,
    ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
    | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f2489]) ).

fof(f2489,plain,
    ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
    | ~ class_Rings_Oidom(t_a) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f67,axiom,
    ( class_Rings_Oidom(t_a)
   => ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C0_C) ).

fof(f9349,plain,
    ! [X0,X1] : c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X0,X1,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
    inference(trivial_inequality_removal,[],[f9348]) ).

fof(f9348,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(t_a) != c_Groups_Ozero__class_Ozero(t_a)
      | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X0,X1,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
    inference(forward_demodulation,[],[f9304,f6684]) ).

fof(f6684,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(t_a) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X0),
    inference(resolution,[],[f5088,f3677]) ).

fof(f5088,plain,
    ! [X2,X0] :
      ( ~ class_Rings_Oidom(X2)
      | c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
    inference(equality_resolution,[],[f4512]) ).

fof(f4512,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
      | ~ class_Rings_Oidom(X2) ),
    inference(cnf_transformation,[],[f3551]) ).

fof(f3551,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
          | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
          | c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(flattening,[],[f3550]) ).

fof(f3550,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
          | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
            & c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
          | c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(nnf_transformation,[],[f2942]) ).

fof(f2942,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) )
      | ~ class_Rings_Oidom(X2) ),
    inference(ennf_transformation,[],[f1870]) ).

fof(f1870,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Oidom(X2)
     => ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) ) ),
    inference(rectify,[],[f69]) ).

fof(f69,axiom,
    ! [X10,X3,X4] :
      ( class_Rings_Oidom(X4)
     => ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Polynomial_Opoly(X4,X3),X10)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X4,X10,X3)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).

fof(f9304,plain,
    ! [X0,X1] :
      ( c_Groups_Ozero__class_Ozero(t_a) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),sK26(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
      | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X0,X1,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
    inference(superposition,[],[f4685,f6684]) ).

fof(f4685,plain,
    ! [X2,X0,X1] :
      ( hAPP(X0,sK26(X0)) != hAPP(X0,sK27(X0))
      | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ),
    inference(cnf_transformation,[],[f3594]) ).

fof(f3594,plain,
    ! [X0,X1,X2] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
      | hAPP(X0,sK26(X0)) != hAPP(X0,sK27(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f3119,f3593]) ).

fof(f3593,plain,
    ! [X0] :
      ( ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4)
     => hAPP(X0,sK26(X0)) != hAPP(X0,sK27(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f3119,plain,
    ! [X0,X1,X2] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
      | ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4) ),
    inference(ennf_transformation,[],[f2290]) ).

fof(f2290,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f1995]) ).

fof(f1995,plain,
    ! [X0,X1,X2] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
    <=> ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X1,X14,X4] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4,X14,X1)
    <=> ! [X2,X15] : hAPP(X1,X2) = hAPP(X1,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_constant__def) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWW246+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n023.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   : Tue Apr 30 03:28:25 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (21556)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.44  % (21559)WARNING: value z3 for option sas not known
% 0.18/0.44  % (21563)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)
% 0.18/0.44  % (21557)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.44  % (21562)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)
% 0.18/0.44  % (21558)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.44  % (21559)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)
% 0.18/0.44  % (21561)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)
% 0.18/0.44  % (21560)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 1.58/0.69  % (21562)First to succeed.
% 1.58/0.69  % (21562)Refutation found. Thanks to Tanya!
% 1.58/0.69  % SZS status ContradictoryAxioms for theBenchmark
% 1.58/0.69  % SZS output start Proof for theBenchmark
% See solution above
% 1.58/0.69  % (21562)------------------------------
% 1.58/0.69  % (21562)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.58/0.69  % (21562)Termination reason: Refutation
% 1.58/0.69  
% 1.58/0.69  % (21562)Memory used [KB]: 6495
% 1.58/0.69  % (21562)Time elapsed: 0.255 s
% 1.58/0.69  % (21562)Instructions burned: 505 (million)
% 1.58/0.69  % (21562)------------------------------
% 1.58/0.69  % (21562)------------------------------
% 1.58/0.69  % (21556)Success in time 0.345 s
%------------------------------------------------------------------------------