TSTP Solution File: GEO051-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO051-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 11:13:23 EDT 2024

% Result   : Unsatisfiable 10.26s 1.82s
% Output   : Refutation 10.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  146 (  31 unt;   0 def)
%            Number of atoms       :  305 (  77 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  288 ( 129   ~; 149   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;  11 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-4 aty)
%            Number of variables   :  158 ( 158   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f31993,plain,
    $false,
    inference(avatar_sat_refutation,[],[f3592,f6918,f11085,f29535,f29907,f31155,f31825,f31827,f31829,f31980]) ).

fof(f31980,plain,
    ~ spl0_10,
    inference(avatar_contradiction_clause,[],[f31979]) ).

fof(f31979,plain,
    ( $false
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f31950,f82]) ).

fof(f82,axiom,
    ~ between(v,x,w),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_between_v_and_w) ).

fof(f31950,plain,
    ( between(v,x,w)
    | ~ spl0_10 ),
    inference(superposition,[],[f4,f31830]) ).

fof(f31830,plain,
    ( w = extension(v,x,x,w)
    | ~ spl0_10 ),
    inference(resolution,[],[f31153,f22399]) ).

fof(f22399,plain,
    ! [X0] :
      ( ~ between(u,x,X0)
      | extension(v,x,x,X0) = X0 ),
    inference(subsumption_resolution,[],[f22310,f639]) ).

fof(f639,plain,
    u != x,
    inference(resolution,[],[f637,f480]) ).

fof(f480,plain,
    ! [X2,X0,X1] :
      ( between(X2,X1,X0)
      | X0 != X1 ),
    inference(duplicate_literal_removal,[],[f477]) ).

fof(f477,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | between(X2,X1,X0)
      | X0 != X1 ),
    inference(superposition,[],[f454,f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( reflection(X0,X1) = X1
      | X0 != X1 ),
    inference(superposition,[],[f36,f44]) ).

fof(f44,axiom,
    ! [X3,X10] : reflection(reflection(X10,X3),X3) = X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).

fof(f36,axiom,
    ! [X3,X10] :
      ( reflection(X10,X3) != X3
      | X3 = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).

fof(f454,plain,
    ! [X2,X0,X1] :
      ( reflection(X0,X1) != X0
      | between(X2,X1,X0) ),
    inference(inner_rewriting,[],[f446]) ).

fof(f446,plain,
    ! [X2,X0,X1] :
      ( reflection(X0,X1) != X0
      | between(X2,X1,reflection(X0,X1)) ),
    inference(resolution,[],[f181,f85]) ).

fof(f85,plain,
    ! [X3,X10,X5] :
      ( ~ between(X10,X5,X10)
      | between(X3,X5,X10) ),
    inference(equality_resolution,[],[f46]) ).

fof(f46,axiom,
    ! [X3,X10,X0,X5] :
      ( X0 != X10
      | ~ between(X10,X5,X0)
      | between(X3,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).

fof(f181,plain,
    ! [X2,X0,X1] :
      ( between(reflection(X0,X1),X1,X2)
      | X0 != X2 ),
    inference(superposition,[],[f158,f44]) ).

fof(f158,plain,
    ! [X2,X0,X1] :
      ( reflection(X0,X1) != X2
      | between(X0,X1,X2) ),
    inference(forward_demodulation,[],[f147,f35]) ).

fof(f35,axiom,
    ! [X10] : reflection(X10,X10) = X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).

fof(f147,plain,
    ! [X2,X0,X1] :
      ( between(X0,X1,reflection(X2,X2))
      | reflection(X0,X1) != X2 ),
    inference(superposition,[],[f32,f120]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( reflection(X1,X1) = X0
      | X0 != X1 ),
    inference(superposition,[],[f44,f104]) ).

fof(f32,axiom,
    ! [X3,X10] : between(X10,X3,reflection(X10,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).

fof(f637,plain,
    ~ between(v,x,u),
    inference(subsumption_resolution,[],[f633,f499]) ).

fof(f499,plain,
    v != x,
    inference(resolution,[],[f487,f82]) ).

fof(f487,plain,
    ! [X2,X0,X1] :
      ( between(X0,X1,X2)
      | X0 != X1 ),
    inference(resolution,[],[f480,f47]) ).

fof(f47,axiom,
    ! [X3,X10,X5] :
      ( ~ between(X10,X3,X5)
      | between(X5,X3,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).

fof(f633,plain,
    ( ~ between(v,x,u)
    | v = x ),
    inference(resolution,[],[f49,f106]) ).

fof(f106,plain,
    between(x,v,u),
    inference(resolution,[],[f47,f79]) ).

fof(f79,axiom,
    between(u,v,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_x) ).

fof(f49,axiom,
    ! [X3,X10,X5] :
      ( ~ between(X10,X3,X5)
      | ~ between(X3,X10,X5)
      | X3 = X10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).

fof(f22310,plain,
    ! [X0] :
      ( u = x
      | ~ between(u,x,X0)
      | extension(v,x,x,X0) = X0 ),
    inference(resolution,[],[f3040,f1927]) ).

fof(f1927,plain,
    ! [X0,X1] : between(u,x,extension(v,x,X0,X1)),
    inference(resolution,[],[f1921,f4]) ).

fof(f1921,plain,
    ! [X0] :
      ( ~ between(v,x,X0)
      | between(u,x,X0) ),
    inference(subsumption_resolution,[],[f1898,f499]) ).

fof(f1898,plain,
    ! [X0] :
      ( v = x
      | ~ between(v,x,X0)
      | between(u,x,X0) ),
    inference(resolution,[],[f55,f79]) ).

fof(f55,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ between(X10,X3,X5)
      | X3 = X5
      | ~ between(X3,X5,X0)
      | between(X10,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).

fof(f3040,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between(X1,X0,extension(X2,X0,X0,X3))
      | X0 = X1
      | ~ between(X1,X0,X3)
      | extension(X2,X0,X0,X3) = X3 ),
    inference(resolution,[],[f39,f5]) ).

fof(f5,axiom,
    ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).

fof(f39,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ equidistant(X3,X5,X3,X0)
      | X3 = X10
      | ~ between(X10,X3,X5)
      | ~ between(X10,X3,X0)
      | X0 = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).

fof(f31153,plain,
    ( between(u,x,w)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f31152]) ).

fof(f31152,plain,
    ( spl0_10
  <=> between(u,x,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f4,axiom,
    ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).

fof(f31829,plain,
    spl0_10,
    inference(avatar_contradiction_clause,[],[f31828]) ).

fof(f31828,plain,
    ( $false
    | spl0_10 ),
    inference(subsumption_resolution,[],[f31822,f81]) ).

fof(f81,axiom,
    ~ between(v,w,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_not_between_v_and_x) ).

fof(f31822,plain,
    ( between(v,w,x)
    | spl0_10 ),
    inference(trivial_inequality_removal,[],[f31802]) ).

fof(f31802,plain,
    ( between(v,w,x)
    | u != u
    | spl0_10 ),
    inference(resolution,[],[f31224,f927]) ).

fof(f927,plain,
    ! [X0] :
      ( between(X0,v,w)
      | u != X0 ),
    inference(resolution,[],[f921,f487]) ).

fof(f921,plain,
    ! [X0] :
      ( ~ between(u,X0,v)
      | between(X0,v,w) ),
    inference(resolution,[],[f54,f78]) ).

fof(f78,axiom,
    between(u,v,w),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).

fof(f54,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ between(X10,X5,X0)
      | ~ between(X10,X3,X5)
      | between(X3,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).

fof(f31224,plain,
    ( ! [X0] :
        ( ~ between(u,X0,w)
        | between(X0,w,x) )
    | spl0_10 ),
    inference(resolution,[],[f31217,f54]) ).

fof(f31217,plain,
    ( between(u,w,x)
    | spl0_10 ),
    inference(subsumption_resolution,[],[f31211,f78]) ).

fof(f31211,plain,
    ( between(u,w,x)
    | ~ between(u,v,w)
    | spl0_10 ),
    inference(resolution,[],[f31154,f3479]) ).

fof(f3479,plain,
    ! [X0] :
      ( between(u,x,X0)
      | between(u,X0,x)
      | ~ between(u,v,X0) ),
    inference(subsumption_resolution,[],[f3447,f80]) ).

fof(f80,axiom,
    u != v,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).

fof(f3447,plain,
    ! [X0] :
      ( u = v
      | ~ between(u,v,X0)
      | between(u,X0,x)
      | between(u,x,X0) ),
    inference(resolution,[],[f77,f79]) ).

fof(f77,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ between(X10,X3,X5)
      | X3 = X10
      | ~ between(X10,X3,X0)
      | between(X10,X0,X5)
      | between(X10,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b12) ).

fof(f31154,plain,
    ( ~ between(u,x,w)
    | spl0_10 ),
    inference(avatar_component_clause,[],[f31152]) ).

fof(f31827,plain,
    spl0_10,
    inference(avatar_contradiction_clause,[],[f31826]) ).

fof(f31826,plain,
    ( $false
    | spl0_10 ),
    inference(subsumption_resolution,[],[f31823,f81]) ).

fof(f31823,plain,
    ( between(v,w,x)
    | spl0_10 ),
    inference(trivial_inequality_removal,[],[f31798]) ).

fof(f31798,plain,
    ( between(v,w,x)
    | w != w
    | spl0_10 ),
    inference(resolution,[],[f31224,f1171]) ).

fof(f1171,plain,
    ! [X0] :
      ( between(u,v,X0)
      | w != X0 ),
    inference(resolution,[],[f1165,f47]) ).

fof(f1165,plain,
    ! [X0] :
      ( between(X0,v,u)
      | w != X0 ),
    inference(resolution,[],[f923,f487]) ).

fof(f923,plain,
    ! [X0] :
      ( ~ between(w,X0,v)
      | between(X0,v,u) ),
    inference(resolution,[],[f54,f105]) ).

fof(f105,plain,
    between(w,v,u),
    inference(resolution,[],[f47,f78]) ).

fof(f31825,plain,
    spl0_10,
    inference(avatar_contradiction_clause,[],[f31824]) ).

fof(f31824,plain,
    ( $false
    | spl0_10 ),
    inference(subsumption_resolution,[],[f31795,f81]) ).

fof(f31795,plain,
    ( between(v,w,x)
    | spl0_10 ),
    inference(resolution,[],[f31224,f78]) ).

fof(f31155,plain,
    ( ~ spl0_9
    | ~ spl0_10
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f31140,f29528,f31152,f31148]) ).

fof(f31148,plain,
    ( spl0_9
  <=> between(x,v,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f29528,plain,
    ( spl0_7
  <=> between(u,w,reflection(u,x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f31140,plain,
    ( ~ between(u,x,w)
    | ~ between(x,v,w)
    | ~ spl0_7 ),
    inference(resolution,[],[f29926,f29010]) ).

fof(f29010,plain,
    ! [X0] :
      ( ~ between(x,X0,reflection(u,x))
      | ~ between(x,v,X0) ),
    inference(subsumption_resolution,[],[f28978,f22531]) ).

fof(f22531,plain,
    ! [X0] :
      ( ~ between(x,v,X0)
      | x != X0 ),
    inference(subsumption_resolution,[],[f22506,f499]) ).

fof(f22506,plain,
    ! [X0] :
      ( ~ between(x,v,X0)
      | v = x
      | x != X0 ),
    inference(superposition,[],[f624,f22441]) ).

fof(f22441,plain,
    ! [X0] :
      ( extension(v,x,x,X0) = X0
      | x != X0 ),
    inference(resolution,[],[f22399,f480]) ).

fof(f624,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between(X0,X1,extension(X1,X0,X2,X3))
      | X0 = X1 ),
    inference(resolution,[],[f49,f4]) ).

fof(f28978,plain,
    ! [X0] :
      ( ~ between(x,v,X0)
      | ~ between(x,X0,reflection(u,x))
      | x = X0 ),
    inference(resolution,[],[f27894,f49]) ).

fof(f27894,plain,
    ! [X0] :
      ( between(X0,x,reflection(u,x))
      | ~ between(x,v,X0) ),
    inference(resolution,[],[f25579,f47]) ).

fof(f25579,plain,
    ! [X0] :
      ( between(reflection(u,x),x,X0)
      | ~ between(x,v,X0) ),
    inference(subsumption_resolution,[],[f25566,f499]) ).

fof(f25566,plain,
    ! [X0] :
      ( v = x
      | ~ between(x,v,X0)
      | between(reflection(u,x),x,X0) ),
    inference(resolution,[],[f25366,f56]) ).

fof(f56,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ between(X10,X3,X5)
      | X3 = X5
      | ~ between(X3,X5,X0)
      | between(X10,X3,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b7) ).

fof(f25366,plain,
    between(reflection(u,x),x,v),
    inference(superposition,[],[f110,f22451]) ).

fof(f22451,plain,
    reflection(u,x) = extension(v,x,x,reflection(u,x)),
    inference(resolution,[],[f22399,f32]) ).

fof(f110,plain,
    ! [X2,X3,X0,X1] : between(extension(X0,X1,X2,X3),X1,X0),
    inference(resolution,[],[f47,f4]) ).

fof(f29926,plain,
    ( ! [X0] :
        ( between(X0,w,reflection(u,x))
        | ~ between(u,X0,w) )
    | ~ spl0_7 ),
    inference(resolution,[],[f29530,f54]) ).

fof(f29530,plain,
    ( between(u,w,reflection(u,x))
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f29528]) ).

fof(f29907,plain,
    spl0_7,
    inference(avatar_contradiction_clause,[],[f29906]) ).

fof(f29906,plain,
    ( $false
    | spl0_7 ),
    inference(subsumption_resolution,[],[f29877,f82]) ).

fof(f29877,plain,
    ( between(v,x,w)
    | spl0_7 ),
    inference(superposition,[],[f4,f29628]) ).

fof(f29628,plain,
    ( w = extension(v,x,x,w)
    | spl0_7 ),
    inference(resolution,[],[f29559,f22399]) ).

fof(f29559,plain,
    ( between(u,x,w)
    | spl0_7 ),
    inference(subsumption_resolution,[],[f29553,f79]) ).

fof(f29553,plain,
    ( between(u,x,w)
    | ~ between(u,v,x)
    | spl0_7 ),
    inference(resolution,[],[f29542,f3478]) ).

fof(f3478,plain,
    ! [X0] :
      ( between(u,w,X0)
      | between(u,X0,w)
      | ~ between(u,v,X0) ),
    inference(subsumption_resolution,[],[f3446,f80]) ).

fof(f3446,plain,
    ! [X0] :
      ( u = v
      | ~ between(u,v,X0)
      | between(u,X0,w)
      | between(u,w,X0) ),
    inference(resolution,[],[f77,f78]) ).

fof(f29542,plain,
    ( ~ between(u,w,x)
    | spl0_7 ),
    inference(resolution,[],[f29529,f1055]) ).

fof(f1055,plain,
    ! [X2,X0,X1] :
      ( between(X0,X1,reflection(X0,X2))
      | ~ between(X0,X1,X2) ),
    inference(resolution,[],[f58,f32]) ).

fof(f58,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ between(X10,X5,X0)
      | ~ between(X10,X3,X5)
      | between(X10,X3,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).

fof(f29529,plain,
    ( ~ between(u,w,reflection(u,x))
    | spl0_7 ),
    inference(avatar_component_clause,[],[f29528]) ).

fof(f29535,plain,
    ( spl0_7
    | ~ spl0_8 ),
    inference(avatar_split_clause,[],[f28763,f29532,f29528]) ).

fof(f29532,plain,
    ( spl0_8
  <=> between(x,w,v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f28763,plain,
    ( ~ between(x,w,v)
    | between(u,w,reflection(u,x)) ),
    inference(resolution,[],[f27768,f1920]) ).

fof(f1920,plain,
    ! [X0] :
      ( ~ between(v,w,X0)
      | between(u,w,X0) ),
    inference(subsumption_resolution,[],[f1897,f500]) ).

fof(f500,plain,
    v != w,
    inference(resolution,[],[f487,f81]) ).

fof(f1897,plain,
    ! [X0] :
      ( v = w
      | ~ between(v,w,X0)
      | between(u,w,X0) ),
    inference(resolution,[],[f55,f78]) ).

fof(f27768,plain,
    ! [X0] :
      ( between(v,X0,reflection(u,x))
      | ~ between(x,X0,v) ),
    inference(resolution,[],[f25567,f47]) ).

fof(f25567,plain,
    ! [X0] :
      ( between(reflection(u,x),X0,v)
      | ~ between(x,X0,v) ),
    inference(resolution,[],[f25366,f57]) ).

fof(f57,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ between(X10,X3,X0)
      | ~ between(X3,X5,X0)
      | between(X10,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).

fof(f11085,plain,
    ( spl0_5
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f7912,f11082,f11078]) ).

fof(f11078,plain,
    ( spl0_5
  <=> u = reflection(v,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f11082,plain,
    ( spl0_6
  <=> between(x,reflection(v,u),u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f7912,plain,
    ( ~ between(x,reflection(v,u),u)
    | u = reflection(v,u) ),
    inference(resolution,[],[f7871,f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ between(X0,X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).

fof(f7871,plain,
    ! [X0] :
      ( between(X0,u,reflection(v,u))
      | ~ between(x,X0,u) ),
    inference(superposition,[],[f915,f7148]) ).

fof(f7148,plain,
    reflection(v,u) = extension(x,u,u,reflection(v,u)),
    inference(resolution,[],[f4361,f32]) ).

fof(f4361,plain,
    ! [X0] :
      ( ~ between(v,u,X0)
      | extension(x,u,u,X0) = X0 ),
    inference(subsumption_resolution,[],[f4348,f639]) ).

fof(f4348,plain,
    ! [X0] :
      ( ~ between(v,u,X0)
      | u = x
      | extension(x,u,u,X0) = X0 ),
    inference(resolution,[],[f1923,f40]) ).

fof(f40,axiom,
    ! [X3,X10,X5] :
      ( ~ between(X10,X3,X5)
      | X3 = X10
      | extension(X10,X3,X3,X5) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).

fof(f1923,plain,
    ! [X0] :
      ( between(x,u,X0)
      | ~ between(v,u,X0) ),
    inference(subsumption_resolution,[],[f1910,f80]) ).

fof(f1910,plain,
    ! [X0] :
      ( u = v
      | ~ between(v,u,X0)
      | between(x,u,X0) ),
    inference(resolution,[],[f55,f106]) ).

fof(f915,plain,
    ! [X2,X3,X0,X1,X4] :
      ( between(X1,X2,extension(X0,X2,X3,X4))
      | ~ between(X0,X1,X2) ),
    inference(resolution,[],[f54,f4]) ).

fof(f6918,plain,
    ( ~ spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f1934,f6915,f6911]) ).

fof(f6911,plain,
    ( spl0_3
  <=> between(u,reflection(v,x),x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f6915,plain,
    ( spl0_4
  <=> x = reflection(v,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f1934,plain,
    ( x = reflection(v,x)
    | ~ between(u,reflection(v,x),x) ),
    inference(resolution,[],[f1928,f50]) ).

fof(f50,axiom,
    ! [X3,X10,X5] :
      ( ~ between(X10,X5,X3)
      | X3 = X5
      | ~ between(X10,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).

fof(f1928,plain,
    between(u,x,reflection(v,x)),
    inference(resolution,[],[f1921,f32]) ).

fof(f3592,plain,
    ( ~ spl0_1
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f3566,f3589,f3585]) ).

fof(f3585,plain,
    ( spl0_1
  <=> v = reflection(v,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f3589,plain,
    ( spl0_2
  <=> between(x,u,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f3566,plain,
    ( ~ between(x,u,w)
    | v != reflection(v,x) ),
    inference(resolution,[],[f3016,f1076]) ).

fof(f1076,plain,
    ! [X0] :
      ( between(u,X0,w)
      | v != X0 ),
    inference(resolution,[],[f994,f487]) ).

fof(f994,plain,
    ! [X0] :
      ( ~ between(v,X0,w)
      | between(u,X0,w) ),
    inference(resolution,[],[f57,f78]) ).

fof(f3016,plain,
    ! [X0] :
      ( ~ between(u,reflection(v,x),X0)
      | ~ between(x,u,X0) ),
    inference(subsumption_resolution,[],[f3000,f981]) ).

fof(f981,plain,
    u != reflection(v,x),
    inference(subsumption_resolution,[],[f979,f499]) ).

fof(f979,plain,
    ( u != reflection(v,x)
    | v = x ),
    inference(resolution,[],[f970,f698]) ).

fof(f698,plain,
    ! [X0,X1] :
      ( ~ between(reflection(X0,X1),X0,X1)
      | X0 = X1 ),
    inference(resolution,[],[f50,f93]) ).

fof(f93,plain,
    ! [X0,X1] : between(reflection(X0,X1),X1,X0),
    inference(superposition,[],[f32,f44]) ).

fof(f970,plain,
    ! [X0] :
      ( between(X0,v,x)
      | u != X0 ),
    inference(resolution,[],[f922,f487]) ).

fof(f922,plain,
    ! [X0] :
      ( ~ between(u,X0,v)
      | between(X0,v,x) ),
    inference(resolution,[],[f54,f79]) ).

fof(f3000,plain,
    ! [X0] :
      ( ~ between(x,u,X0)
      | ~ between(u,reflection(v,x),X0)
      | u = reflection(v,x) ),
    inference(resolution,[],[f1961,f49]) ).

fof(f1961,plain,
    ! [X0] :
      ( between(reflection(v,x),u,X0)
      | ~ between(x,u,X0) ),
    inference(subsumption_resolution,[],[f1952,f639]) ).

fof(f1952,plain,
    ! [X0] :
      ( u = x
      | ~ between(x,u,X0)
      | between(reflection(v,x),u,X0) ),
    inference(resolution,[],[f1932,f55]) ).

fof(f1932,plain,
    between(reflection(v,x),x,u),
    inference(resolution,[],[f1928,f47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : GEO051-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 05:49:28 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (21052)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (21055)WARNING: value z3 for option sas not known
% 0.14/0.38  % (21053)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (21054)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (21056)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (21055)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)
% 0.14/0.38  % (21057)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)
% 0.14/0.38  % (21058)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)
% 0.14/0.38  % (21059)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)
% 0.14/0.38  Detected minimum model sizes of [3]
% 0.14/0.38  Detected maximum model sizes of [max]
% 0.14/0.39  TRYING [3]
% 0.20/0.42  Detected minimum model sizes of [3]
% 0.20/0.42  Detected maximum model sizes of [max]
% 0.20/0.46  TRYING [3]
% 0.20/0.50  TRYING [4]
% 5.20/1.16  TRYING [5]
% 6.84/1.37  TRYING [4]
% 7.93/1.48  Detected minimum model sizes of [3]
% 7.93/1.48  Detected maximum model sizes of [max]
% 7.93/1.48  TRYING [3]
% 8.13/1.52  TRYING [4]
% 10.26/1.82  % (21055)First to succeed.
% 10.26/1.82  % (21055)Refutation found. Thanks to Tanya!
% 10.26/1.82  % SZS status Unsatisfiable for theBenchmark
% 10.26/1.82  % SZS output start Proof for theBenchmark
% See solution above
% 10.26/1.82  % (21055)------------------------------
% 10.26/1.82  % (21055)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 10.26/1.82  % (21055)Termination reason: Refutation
% 10.26/1.82  
% 10.26/1.82  % (21055)Memory used [KB]: 19728
% 10.26/1.82  % (21055)Time elapsed: 1.445 s
% 10.26/1.82  % (21055)Instructions burned: 4676 (million)
% 10.26/1.82  % (21055)------------------------------
% 10.26/1.82  % (21055)------------------------------
% 10.26/1.82  % (21052)Success in time 1.429 s
%------------------------------------------------------------------------------