TSTP Solution File: SWW213+1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWW213+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n028.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 Sep  1 01:00:23 EDT 2023

% Result   : Theorem 0.32s 0.62s
% Output   : Refutation 0.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (   9 unt;   0 def)
%            Number of atoms       :   58 (  23 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   55 (  27   ~;  18   |;   0   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   51 (;  48   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7006,plain,
    $false,
    inference(subsumption_resolution,[],[f6976,f4384]) ).

fof(f4384,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1181]) ).

fof(f1181,axiom,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/tmp/tmp.kgYXxz2uLC/Vampire---4.8_797',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

fof(f6976,plain,
    ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(resolution,[],[f6974,f6724]) ).

fof(f6724,plain,
    ! [X2,X0,X1] :
      ( sQ138_eqProxy(c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(equality_proxy_replacement,[],[f5439,f6238]) ).

fof(f6238,plain,
    ! [X0,X1] :
      ( sQ138_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ138_eqProxy])]) ).

fof(f5439,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(cnf_transformation,[],[f2981]) ).

fof(f2981,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f1943]) ).

fof(f1943,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Polynomial_Odegree(X2,X1) = c_Polynomial_Odegree(X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X0)) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X7,X5,X6] :
      ( class_Rings_Ocomm__semiring__0(X6)
     => c_Polynomial_Odegree(X6,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X5,X7)) = c_Polynomial_Odegree(X6,X5) ),
    file('/export/starexec/sandbox/tmp/tmp.kgYXxz2uLC/Vampire---4.8_797',fact_degree__offset__poly) ).

fof(f6974,plain,
    ~ sQ138_eqProxy(c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_z))),
    inference(subsumption_resolution,[],[f6943,f4384]) ).

fof(f6943,plain,
    ( ~ sQ138_eqProxy(c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_z)))
    | ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
    inference(resolution,[],[f6942,f6867]) ).

fof(f6867,plain,
    ! [X2,X3,X0,X1] :
      ( sQ138_eqProxy(hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0),hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(equality_proxy_replacement,[],[f5851,f6238]) ).

fof(f5851,plain,
    ! [X2,X3,X0,X1] :
      ( hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f3341]) ).

fof(f3341,plain,
    ! [X0,X1,X2,X3] :
      ( hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f2193]) ).

fof(f2193,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => hAPP(c_Polynomial_Opoly(X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X2,X1)),X0) = hAPP(c_Polynomial_Opoly(X3,X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X3,X7,X5,X6] :
      ( class_Rings_Ocomm__semiring__0(X6)
     => hAPP(c_Polynomial_Opoly(X6,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X6,X5,X7)),X3) = hAPP(c_Polynomial_Opoly(X6,X5),c_Groups_Oplus__class_Oplus(X6,X7,X3)) ),
    file('/export/starexec/sandbox/tmp/tmp.kgYXxz2uLC/Vampire---4.8_797',fact_poly__offset__poly) ).

fof(f6942,plain,
    ! [X0] :
      ( ~ sQ138_eqProxy(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK103(X0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,sK103(X0))))
      | ~ sQ138_eqProxy(c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0)) ),
    inference(subsumption_resolution,[],[f6243,f4204]) ).

fof(f4204,plain,
    ~ v_thesis____,
    inference(cnf_transformation,[],[f1266]) ).

fof(f1266,plain,
    ~ v_thesis____,
    inference(flattening,[],[f1265]) ).

fof(f1265,negated_conjecture,
    ~ v_thesis____,
    inference(negated_conjecture,[],[f1264]) ).

fof(f1264,conjecture,
    v_thesis____,
    file('/export/starexec/sandbox/tmp/tmp.kgYXxz2uLC/Vampire---4.8_797',conj_1) ).

fof(f6243,plain,
    ! [X0] :
      ( v_thesis____
      | ~ sQ138_eqProxy(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK103(X0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,sK103(X0))))
      | ~ sQ138_eqProxy(c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),c_Polynomial_Odegree(tc_Complex_Ocomplex,X0)) ),
    inference(equality_proxy_replacement,[],[f4205,f6238,f6238]) ).

fof(f4205,plain,
    ! [X0] :
      ( v_thesis____
      | hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK103(X0)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,sK103(X0)))
      | c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) ),
    inference(cnf_transformation,[],[f3679]) ).

fof(f3679,plain,
    ! [X0] :
      ( v_thesis____
      | hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK103(X0)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,sK103(X0)))
      | c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK103])],[f2316,f3678]) ).

fof(f3678,plain,
    ! [X0] :
      ( ? [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1))
     => hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK103(X0)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,sK103(X0))) ),
    introduced(choice_axiom,[]) ).

fof(f2316,plain,
    ! [X0] :
      ( v_thesis____
      | ? [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1))
      | c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) ),
    inference(flattening,[],[f2315]) ).

fof(f2315,plain,
    ! [X0] :
      ( v_thesis____
      | ? [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1))
      | c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) ),
    inference(ennf_transformation,[],[f1267]) ).

fof(f1267,plain,
    ! [X0] :
      ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X0)
     => ( ! [X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X1))
       => v_thesis____ ) ),
    inference(rectify,[],[f1263]) ).

fof(f1263,axiom,
    ! [X18] :
      ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X18) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
     => ( ! [X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X18),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X2))
       => v_thesis____ ) ),
    file('/export/starexec/sandbox/tmp/tmp.kgYXxz2uLC/Vampire---4.8_797',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.24  % Problem    : SWW213+1 : TPTP v8.1.2. Released v5.2.0.
% 0.25/0.25  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.25/0.46  % Computer : n028.cluster.edu
% 0.25/0.46  % Model    : x86_64 x86_64
% 0.25/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.46  % Memory   : 8042.1875MB
% 0.25/0.46  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.25/0.46  % CPULimit   : 300
% 0.25/0.46  % WCLimit    : 300
% 0.25/0.46  % DateTime   : Sun Aug 27 22:27:09 EDT 2023
% 0.25/0.46  % CPUTime    : 
% 0.25/0.46  This is a FOF_THM_RFO_SEQ problem
% 0.25/0.47  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.kgYXxz2uLC/Vampire---4.8_797
% 0.25/0.47  % (930)Running in auto input_syntax mode. Trying TPTP
% 0.32/0.58  % (938)dis+1011_3:2_av=off:ep=RST:fsd=off:fde=none:gsp=on:nm=2:nwc=2.0:sos=on:sp=reverse_frequency_405 on Vampire---4 for (405ds/0Mi)
% 0.32/0.58  % (931)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_1064 on Vampire---4 for (1064ds/0Mi)
% 0.32/0.58  % (934)dis-1010_4:3_afr=on:amm=off:bsr=on:bce=on:drc=off:fsd=off:fde=unused:gs=on:gsaa=from_current:irw=on:nwc=1.3:nicw=on:sas=z3:tgt=full:urr=ec_only_619 on Vampire---4 for (619ds/0Mi)
% 0.32/0.58  % (936)lrs+1002_9_av=off:bs=on:bsr=on:bce=on:cond=on:drc=off:er=filter:flr=on:fsd=off:fsr=off:fde=unused:lcm=predicate:nm=2:nwc=1.3:sims=off:stl=62_466 on Vampire---4 for (466ds/0Mi)
% 0.32/0.58  % (937)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_432 on Vampire---4 for (432ds/0Mi)
% 0.32/0.58  % (932)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_957 on Vampire---4 for (957ds/0Mi)
% 0.32/0.59  % (933)lrs+1010_4_aac=none:add=off:afr=on:amm=off:anc=all_dependent:bd=off:cond=on:drc=off:flr=on:fde=none:gs=on:lma=on:nm=16:nwc=1.1:sims=off:sos=all:sac=on:sp=occurrence:stl=188_669 on Vampire---4 for (669ds/0Mi)
% 0.32/0.62  % (938)First to succeed.
% 0.32/0.62  % (938)Refutation found. Thanks to Tanya!
% 0.32/0.62  % SZS status Theorem for Vampire---4
% 0.32/0.62  % SZS output start Proof for Vampire---4
% See solution above
% 0.32/0.62  % (938)------------------------------
% 0.32/0.62  % (938)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.32/0.62  % (938)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.32/0.62  % (938)Termination reason: Refutation
% 0.32/0.62  
% 0.32/0.62  % (938)Memory used [KB]: 5117
% 0.32/0.62  % (938)Time elapsed: 0.041 s
% 0.32/0.62  % (938)------------------------------
% 0.32/0.62  % (938)------------------------------
% 0.32/0.62  % (930)Success in time 0.151 s
% 0.32/0.62  % Vampire---4.8 exiting
%------------------------------------------------------------------------------