%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWV677-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n009.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 : Wed Aug 31 18:53:48 EDT 2022

% Result   : Unsatisfiable 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   39 (   3 unt;   0 def)
%            Number of atoms       :   96 (  24 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  101 (  44   ~;  50   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   8 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :   12 (  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f790,plain,
    $false,
    inference(avatar_sat_refutation,[],[f698,f699,f711,f722,f724,f750,f759,f789]) ).

fof(f789,plain,
    ( spl0_5
    | ~ spl0_4
    | ~ spl0_6
    | spl0_11 ),
    inference(avatar_split_clause,[],[f788,f755,f713,f704,f708]) ).

fof(f708,plain,
    ( spl0_5
  <=> v_a = c_HOL_Ozero__class_Ozero(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f704,plain,
    ( spl0_4
  <=> class_Ring__and__Field_Ofield(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f713,plain,
    ( spl0_6
  <=> c_lessequals(v_m,v_n,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f755,plain,
    ( spl0_11
  <=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f788,plain,
    ( ~ c_lessequals(v_m,v_n,tc_nat)
    | ~ class_Ring__and__Field_Ofield(t_a)
    | v_a = c_HOL_Ozero__class_Ozero(t_a)
    | spl0_11 ),
    inference(trivial_inequality_removal,[],[f786]) ).

fof(f786,plain,
    ( ~ class_Ring__and__Field_Ofield(t_a)
    | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a)
    | ~ c_lessequals(v_m,v_n,tc_nat)
    | v_a = c_HOL_Ozero__class_Ozero(t_a)
    | spl0_11 ),
    inference(superposition,[],[f757,f568]) ).

fof(f568,axiom,
    ! [X0,X1,X8,X7] :
      ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X8,X7,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X7,X0),c_Power_Opower__class_Opower(X1,X8,X0),X0)
      | ~ c_lessequals(X7,X8,tc_nat)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff__inverse_0) ).

fof(f757,plain,
    ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a)
    | spl0_11 ),
    inference(avatar_component_clause,[],[f755]) ).

fof(f759,plain,
    ( ~ spl0_11
    | ~ spl0_4
    | spl0_1 ),
    inference(avatar_split_clause,[],[f752,f686,f704,f755]) ).

fof(f686,plain,
    ( spl0_1
  <=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f752,plain,
    ( ~ class_Ring__and__Field_Ofield(t_a)
    | c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a)
    | spl0_1 ),
    inference(superposition,[],[f688,f556]) ).

fof(f556,axiom,
    ! [X0,X1] :
      ( c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)
      | ~ class_Ring__and__Field_Ofield(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).

fof(f688,plain,
    ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f686]) ).

fof(f750,plain,
    ( ~ spl0_4
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f745,f708,f704]) ).

fof(f745,plain,
    ( ~ class_Ring__and__Field_Ofield(t_a)
    | ~ spl0_5 ),
    inference(trivial_inequality_removal,[],[f743]) ).

fof(f743,plain,
    ( v_a != v_a
    | ~ class_Ring__and__Field_Ofield(t_a)
    | ~ spl0_5 ),
    inference(superposition,[],[f426,f710]) ).

fof(f710,plain,
    ( v_a = c_HOL_Ozero__class_Ozero(t_a)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f708]) ).

fof(f426,axiom,
    ( v_a != c_HOL_Ozero__class_Ozero(t_a)
    | ~ class_Ring__and__Field_Ofield(t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nz_0) ).

fof(f724,plain,
    ( spl0_6
    | spl0_3 ),
    inference(avatar_split_clause,[],[f723,f695,f713]) ).

fof(f695,plain,
    ( spl0_3
  <=> c_lessequals(v_n,v_m,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f723,plain,
    ( c_lessequals(v_m,v_n,tc_nat)
    | spl0_3 ),
    inference(resolution,[],[f696,f604]) ).

fof(f604,axiom,
    ! [X8,X7] :
      ( c_lessequals(X8,X7,tc_nat)
      | c_lessequals(X7,X8,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

fof(f696,plain,
    ( ~ c_lessequals(v_n,v_m,tc_nat)
    | spl0_3 ),
    inference(avatar_component_clause,[],[f695]) ).

fof(f722,plain,
    spl0_4,
    inference(avatar_contradiction_clause,[],[f721]) ).

fof(f721,plain,
    ( $false
    | spl0_4 ),
    inference(resolution,[],[f706,f638]) ).

fof(f638,axiom,
    class_Ring__and__Field_Ofield(t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).

fof(f706,plain,
    ( ~ class_Ring__and__Field_Ofield(t_a)
    | spl0_4 ),
    inference(avatar_component_clause,[],[f704]) ).

fof(f711,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | spl0_5
    | spl0_2 ),
    inference(avatar_split_clause,[],[f702,f690,f708,f704,f695]) ).

fof(f690,plain,
    ( spl0_2
  <=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f702,plain,
    ( v_a = c_HOL_Ozero__class_Ozero(t_a)
    | ~ class_Ring__and__Field_Ofield(t_a)
    | ~ c_lessequals(v_n,v_m,tc_nat)
    | spl0_2 ),
    inference(trivial_inequality_removal,[],[f701]) ).

fof(f701,plain,
    ( ~ c_lessequals(v_n,v_m,tc_nat)
    | ~ class_Ring__and__Field_Ofield(t_a)
    | c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a)
    | v_a = c_HOL_Ozero__class_Ozero(t_a)
    | spl0_2 ),
    inference(superposition,[],[f692,f603]) ).

fof(f603,axiom,
    ! [X0,X1,X8,X7] :
      ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X7,X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X7,X8,tc_nat),X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | ~ c_lessequals(X8,X7,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff_0) ).

fof(f692,plain,
    ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a)
    | spl0_2 ),
    inference(avatar_component_clause,[],[f690]) ).

fof(f699,plain,
    ( ~ spl0_3
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f640,f690,f695]) ).

fof(f640,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a)
    | ~ c_lessequals(v_n,v_m,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f698,plain,
    ( spl0_3
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f639,f686,f695]) ).

fof(f639,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a)
    | c_lessequals(v_n,v_m,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWV677-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 19:47:50 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.53  % (26591)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=5:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.53  % (26601)lrs+1010_1:1_bd=off:fsr=off:sd=1:sos=on:ss=axioms:i=67:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/67Mi)
% 0.20/0.54  % (26596)lrs+1_1:1_aac=none:add=large:anc=all_dependent:cond=fast:ep=RST:fsr=off:lma=on:nm=2:sos=on:sp=reverse_arity:stl=30:uhcvi=on:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.54  % (26591)Instruction limit reached!
% 0.20/0.54  % (26591)------------------------------
% 0.20/0.54  % (26591)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (26581)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.20/0.54  % (26595)fmb+10_1:1_fmbes=contour:fmbsr=2.0:fmbsso=input_usage:i=6:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.54  % (26596)Instruction limit reached!
% 0.20/0.54  % (26596)------------------------------
% 0.20/0.54  % (26596)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (26596)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (26596)Termination reason: Unknown
% 0.20/0.54  % (26596)Termination phase: Equality proxy
% 0.20/0.54  
% 0.20/0.54  % (26596)Memory used [KB]: 1918
% 0.20/0.54  % (26596)Time elapsed: 0.005 s
% 0.20/0.54  % (26596)Instructions burned: 3 (million)
% 0.20/0.54  % (26596)------------------------------
% 0.20/0.54  % (26596)------------------------------
% 0.20/0.54  % (26584)lrs+1010_1:4_amm=off:bce=on:sd=1:sos=on:ss=included:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (26591)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (26591)Termination reason: Unknown
% 0.20/0.54  % (26591)Termination phase: Saturation
% 0.20/0.54  
% 0.20/0.54  % (26591)Memory used [KB]: 6524
% 0.20/0.55  % (26591)Time elapsed: 0.004 s
% 0.20/0.55  % (26591)Instructions burned: 5 (million)
% 0.20/0.55  % (26591)------------------------------
% 0.20/0.55  % (26591)------------------------------
% 0.20/0.55  % (26601)First to succeed.
% 0.20/0.55  % (26595)Instruction limit reached!
% 0.20/0.55  % (26595)------------------------------
% 0.20/0.55  % (26595)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (26595)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (26595)Termination reason: Unknown
% 0.20/0.55  % (26595)Termination phase: Finite model building preprocessing
% 0.20/0.55  
% 0.20/0.55  % (26595)Memory used [KB]: 2046
% 0.20/0.55  % (26595)Time elapsed: 0.008 s
% 0.20/0.55  % (26595)Instructions burned: 6 (million)
% 0.20/0.55  % (26595)------------------------------
% 0.20/0.55  % (26595)------------------------------
% 0.20/0.55  % (26601)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (26601)------------------------------
% 0.20/0.55  % (26601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (26601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (26601)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (26601)Memory used [KB]: 6524
% 0.20/0.55  % (26601)Time elapsed: 0.068 s
% 0.20/0.55  % (26601)Instructions burned: 8 (million)
% 0.20/0.55  % (26601)------------------------------
% 0.20/0.55  % (26601)------------------------------
% 0.20/0.55  % (26552)Success in time 0.199 s
%------------------------------------------------------------------------------