TSTP Solution File: SWW185+1 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW185+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n027.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 : Mon Jun 24 18:31:29 EDT 2024

% Result   : Theorem 0.22s 0.52s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   41 (  13 unt;   0 def)
%            Number of atoms       :   76 (  42 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   65 (  30   ~;  24   |;   0   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   48 (  48   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3543,plain,
    $false,
    inference(avatar_sat_refutation,[],[f3285,f3441,f3542]) ).

fof(f3542,plain,
    ~ spl23_2,
    inference(avatar_contradiction_clause,[],[f3541]) ).

fof(f3541,plain,
    ( $false
    | ~ spl23_2 ),
    inference(subsumption_resolution,[],[f3540,f2360]) ).

fof(f2360,plain,
    class_Rings_Ocomm__semiring__0(t_a),
    inference(cnf_transformation,[],[f1184]) ).

fof(f1184,axiom,
    class_Rings_Ocomm__semiring__0(t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f3540,plain,
    ( ~ class_Rings_Ocomm__semiring__0(t_a)
    | ~ spl23_2 ),
    inference(subsumption_resolution,[],[f3531,f3442]) ).

fof(f3442,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ spl23_2 ),
    inference(backward_demodulation,[],[f2359,f3284]) ).

fof(f3284,plain,
    ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ spl23_2 ),
    inference(avatar_component_clause,[],[f3282]) ).

fof(f3282,plain,
    ( spl23_2
  <=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl23_2])]) ).

fof(f2359,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_a,v_p),
    inference(cnf_transformation,[],[f1185]) ).

fof(f1185,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_a,v_p),
    inference(flattening,[],[f1183]) ).

fof(f1183,negated_conjecture,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Polynomial_OpCons(t_a,v_a,v_p),
    inference(negated_conjecture,[],[f1182]) ).

fof(f1182,conjecture,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,v_a,v_p),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f3531,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | ~ class_Rings_Ocomm__semiring__0(t_a)
    | ~ spl23_2 ),
    inference(superposition,[],[f2522,f3443]) ).

fof(f3443,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h)
    | ~ spl23_2 ),
    inference(backward_demodulation,[],[f2361,f3284]) ).

fof(f2361,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h),
    inference(cnf_transformation,[],[f1181]) ).

fof(f1181,axiom,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f2522,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(cnf_transformation,[],[f1841]) ).

fof(f1841,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f1295]) ).

fof(f1295,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X3,X5,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Polynomial_OpCons(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Polynomial_OpCons(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f3441,plain,
    spl23_1,
    inference(avatar_split_clause,[],[f3440,f3278]) ).

fof(f3278,plain,
    ( spl23_1
  <=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl23_1])]) ).

fof(f3440,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(subsumption_resolution,[],[f3381,f2360]) ).

fof(f3381,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(trivial_inequality_removal,[],[f3357]) ).

fof(f3357,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(superposition,[],[f2472,f3289]) ).

fof(f3289,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),
    inference(subsumption_resolution,[],[f3286,f2360]) ).

fof(f3286,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(superposition,[],[f2361,f2520]) ).

fof(f2520,plain,
    ! [X2,X3,X0,X1] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f1839]) ).

fof(f1839,plain,
    ! [X0,X1,X2,X3] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f1293]) ).

fof(f1293,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0))) ),
    inference(rectify,[],[f80]) ).

fof(f80,axiom,
    ! [X3,X24,X5,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Polynomial_OpCons(X4,X5,X24),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X24,X3)),c_Polynomial_OpCons(X4,X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X24,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f2472,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f1796]) ).

fof(f1796,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(flattening,[],[f1795]) ).

fof(f1795,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f1253]) ).

fof(f1253,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ),
    inference(rectify,[],[f75]) ).

fof(f75,axiom,
    ! [X5,X24,X22,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X22,X24),c_Polynomial_OpCons(X4,X5,X24))
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X24 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

fof(f3285,plain,
    ( ~ spl23_1
    | spl23_2 ),
    inference(avatar_split_clause,[],[f2362,f3282,f3278]) ).

fof(f2362,plain,
    ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(cnf_transformation,[],[f1748]) ).

fof(f1748,plain,
    ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(ennf_transformation,[],[f1180]) ).

fof(f1180,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
   => v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWW185+1 : TPTP v8.2.0. Released v5.2.0.
% 0.10/0.12  % Command    : run_vampire %s %d THM
% 0.13/0.34  % Computer : n027.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   : Wed Jun 19 07:47:39 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.36  Running first-order theorem proving
% 0.13/0.36  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.48  % (25181)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (25184)lrs+11_1:12_to=lpo:sil=128000:sp=const_min:i=103397:ss=included:sgt=16:av=off:fsd=on:nm=16_0 on theBenchmark for (2999ds/103397Mi)
% 0.22/0.48  % (25181)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (25182)lrs+10_1:628_anc=all_dependent:bsr=unit_only:sil=256000:sp=frequency:i=136310:newcnf=on_0 on theBenchmark for (2999ds/136310Mi)
% 0.22/0.48  % (25181)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (25185)dis+2_1:50_sil=256000:flr=on:sac=on:i=218245:fsr=off:uhcvi=on_0 on theBenchmark for (2999ds/218245Mi)
% 0.22/0.48  % (25181)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (25186)lrs-1010_1:1_sil=2000:i=250:sd=1:ss=axioms:sgt=32:sos=on_0 on theBenchmark for (2999ds/250Mi)
% 0.22/0.48  % (25181)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (25187)lrs-1011_8:1_sil=16000:sos=all:i=346:sd=1:ep=R:ss=axioms_0 on theBenchmark for (2999ds/346Mi)
% 0.22/0.48  % (25181)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (25183)lrs+2_3:1_to=lpo:sil=256000:irw=on:fde=unused:sp=unary_first:bce=on:nwc=6.0:s2agt=30:newcnf=on:s2a=on:i=140573:nm=2_0 on theBenchmark for (2999ds/140573Mi)
% 0.22/0.48  % (25181)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.48  % (25188)lrs+1002_1:1_to=lpo:sil=2000:sp=frequency:sos=on:st=3.0:i=282:sd=2:ss=axioms_0 on theBenchmark for (2999ds/282Mi)
% 0.22/0.48  % (25186)Refutation not found, incomplete strategy% (25186)------------------------------
% 0.22/0.48  % (25186)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.48  % (25186)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.48  % (25186)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.48  
% 0.22/0.48  % (25186)Memory used [KB]: 1917
% 0.22/0.48  % (25186)Time elapsed: 0.009 s
% 0.22/0.48  % (25186)Instructions burned: 9 (million)
% 0.22/0.48  % (25186)------------------------------
% 0.22/0.48  % (25186)------------------------------
% 0.22/0.52  % (25188)First to succeed.
% 0.22/0.52  % (25188)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25181"
% 0.22/0.52  % (25181)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.52  % (25188)Refutation found. Thanks to Tanya!
% 0.22/0.52  % SZS status Theorem for theBenchmark
% 0.22/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.52  % (25188)------------------------------
% 0.22/0.52  % (25188)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.52  % (25188)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.52  % (25188)Termination reason: Refutation
% 0.22/0.52  
% 0.22/0.52  % (25188)Memory used [KB]: 3411
% 0.22/0.52  % (25188)Time elapsed: 0.046 s
% 0.22/0.52  % (25188)Instructions burned: 91 (million)
% 0.22/0.52  % (25188)------------------------------
% 0.22/0.52  % (25188)------------------------------
% 0.22/0.52  % (25181)Success in time 0.11 s
%------------------------------------------------------------------------------