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Vampire---5.0.1.UNS-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SYN181-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 01:49:51 PM UTC 2026

% Result   : Unsatisfiable 0.83s 0.95s
% Output   : Refutation 2.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   42
% Syntax   : Number of formulae    :  140 (  37 unt;  17 def)
%            Number of atoms       :  321 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  365 ( 184   ~; 164   |;   0   &)
%                                         (  17 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   34 (  33 usr;  18 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   88 (   0 sgn  88   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    s0(d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f9,axiom,
    r0(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

fof(f10,axiom,
    p0(b,d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

fof(f11,axiom,
    n0(e,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).

fof(f14,axiom,
    ! [X0] : p0(b,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).

fof(f17,axiom,
    ! [X0] : q0(X0,d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).

fof(f19,axiom,
    ! [X0,X1] : m0(X0,d,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).

fof(f24,axiom,
    l0(c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).

fof(f26,axiom,
    n0(d,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).

fof(f34,axiom,
    n0(c,d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).

fof(f36,axiom,
    q0(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_36) ).

fof(f39,axiom,
    ! [X0,X1] :
      ( ~ n0(X1,X0)
      | k1(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_001) ).

fof(f40,axiom,
    ! [X0,X1] :
      ( l1(X0,X0)
      | ~ n0(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).

fof(f41,axiom,
    ! [X2,X3,X0,X1] :
      ( l1(X0,X1)
      | ~ p0(X2,X0)
      | ~ r0(X3)
      | ~ m0(X1,X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_003) ).

fof(f42,axiom,
    ! [X0,X1] :
      ( l1(X0,X0)
      | ~ k1(X0)
      | ~ l0(X1)
      | ~ l1(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_004) ).

fof(f163,axiom,
    ! [X0] :
      ( ~ p0(X0,X0)
      | s1(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_125) ).

fof(f164,axiom,
    ! [X2,X0,X1] :
      ( s1(X0)
      | ~ q0(X0,X1)
      | ~ s1(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_126) ).

fof(f169,axiom,
    ! [X0,X1] :
      ( l2(X0,X1)
      | ~ s1(X0)
      | ~ n0(e,X1)
      | ~ l2(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_131) ).

fof(f171,axiom,
    ! [X2,X3,X0,X1] :
      ( l2(X0,X0)
      | ~ p0(X1,X1)
      | ~ s1(X2)
      | ~ m0(X3,X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_133) ).

fof(f224,axiom,
    ! [X0,X1] :
      ( q2(X0,X0,X1)
      | ~ l1(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_186) ).

fof(f228,axiom,
    ( s2(d)
    | ~ s1(a)
    | ~ s0(d) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_190) ).

fof(f231,axiom,
    ! [X0,X1] :
      ( k3(X0,X0,X0)
      | ~ s1(X0)
      | ~ q2(d,X1,d)
      | ~ s2(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_193) ).

fof(f277,axiom,
    ( m3(b,b,b)
    | ~ l2(a,b) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_239) ).

fof(f333,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ m3(X3,X4,X3)
      | ~ k3(X2,X2,X0)
      | ~ q2(X3,X1,X0)
      | q4(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_295) ).

fof(f369,negated_conjecture,
    ~ q4(d,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

fof(f694,definition,
    ( spl0_94
  <=> ! [X1] : ~ s1(X1) ),
    introduced(definition,[new_symbols(definition,[spl0_94])],[avatar_definition]) ).

fof(f695,plain,
    ( ! [X1] : ~ s1(X1)
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f694]) ).

fof(f755,definition,
    ( spl0_111
  <=> s2(d) ),
    introduced(definition,[new_symbols(definition,[spl0_111])],[avatar_definition]) ).

fof(f800,definition,
    ( spl0_124
  <=> ! [X0,X1] :
        ( s1(X0)
        | ~ q0(X0,X1) ) ),
    introduced(definition,[new_symbols(definition,[spl0_124])],[avatar_definition]) ).

fof(f801,plain,
    ( ! [X0,X1] :
        ( ~ q0(X0,X1)
        | s1(X0) )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f800]) ).

fof(f802,plain,
    ( spl0_94
    | spl0_124 ),
    inference(avatar_split_clause,[],[f164,f800,f694]) ).

fof(f804,definition,
    ( spl0_125
  <=> ! [X1] : ~ p0(X1,X1) ),
    introduced(definition,[new_symbols(definition,[spl0_125])],[avatar_definition]) ).

fof(f805,plain,
    ( ! [X1] : ~ p0(X1,X1)
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f804]) ).

fof(f807,definition,
    ( spl0_126
  <=> ! [X2,X0,X3] :
        ( l2(X0,X0)
        | ~ s1(X2)
        | ~ m0(X3,X2,X0) ) ),
    introduced(definition,[new_symbols(definition,[spl0_126])],[avatar_definition]) ).

fof(f808,plain,
    ( ! [X2,X3,X0] :
        ( l2(X0,X0)
        | ~ s1(X2)
        | ~ m0(X3,X2,X0) )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f807]) ).

fof(f809,plain,
    ( spl0_125
    | spl0_126 ),
    inference(avatar_split_clause,[],[f171,f807,f804]) ).

fof(f828,definition,
    ( spl0_132
  <=> s0(d) ),
    introduced(definition,[new_symbols(definition,[spl0_132])],[avatar_definition]) ).

fof(f829,plain,
    ( ~ s0(d)
    | spl0_132 ),
    inference(avatar_component_clause,[],[f828]) ).

fof(f831,definition,
    ( spl0_133
  <=> s1(a) ),
    introduced(definition,[new_symbols(definition,[spl0_133])],[avatar_definition]) ).

fof(f832,plain,
    ( ~ s1(a)
    | spl0_133 ),
    inference(avatar_component_clause,[],[f831]) ).

fof(f833,plain,
    ( s2(d)
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f755]) ).

fof(f834,plain,
    ( ~ spl0_132
    | ~ spl0_133
    | spl0_111 ),
    inference(avatar_split_clause,[],[f228,f755,f831,f828]) ).

fof(f836,definition,
    ( spl0_134
  <=> ! [X1] :
        ( ~ q2(d,X1,d)
        | ~ s2(X1) ) ),
    introduced(definition,[new_symbols(definition,[spl0_134])],[avatar_definition]) ).

fof(f837,plain,
    ( ! [X1] :
        ( ~ q2(d,X1,d)
        | ~ s2(X1) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f836]) ).

fof(f839,definition,
    ( spl0_135
  <=> ! [X0] :
        ( k3(X0,X0,X0)
        | ~ s1(X0) ) ),
    introduced(definition,[new_symbols(definition,[spl0_135])],[avatar_definition]) ).

fof(f840,plain,
    ( ! [X0] :
        ( k3(X0,X0,X0)
        | ~ s1(X0) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f839]) ).

fof(f841,plain,
    ( spl0_134
    | spl0_135 ),
    inference(avatar_split_clause,[],[f231,f839,f836]) ).

fof(f952,definition,
    ( spl0_166
  <=> ! [X0] : ~ r0(X0) ),
    introduced(definition,[new_symbols(definition,[spl0_166])],[avatar_definition]) ).

fof(f953,plain,
    ( ! [X0] : ~ r0(X0)
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f952]) ).

fof(f999,definition,
    ( spl0_179
  <=> l2(a,b) ),
    introduced(definition,[new_symbols(definition,[spl0_179])],[avatar_definition]) ).

fof(f1000,plain,
    ( ~ l2(a,b)
    | spl0_179 ),
    inference(avatar_component_clause,[],[f999]) ).

fof(f1002,definition,
    ( spl0_180
  <=> m3(b,b,b) ),
    introduced(definition,[new_symbols(definition,[spl0_180])],[avatar_definition]) ).

fof(f1003,plain,
    ( m3(b,b,b)
    | ~ spl0_180 ),
    inference(avatar_component_clause,[],[f1002]) ).

fof(f1004,plain,
    ( ~ spl0_179
    | spl0_180 ),
    inference(avatar_split_clause,[],[f277,f1002,f999]) ).

fof(f1106,definition,
    ( spl0_209
  <=> ! [X2,X0,X1] :
        ( l1(X0,X1)
        | ~ m0(X1,X0,X2)
        | ~ p0(X2,X0) ) ),
    introduced(definition,[new_symbols(definition,[spl0_209])],[avatar_definition]) ).

fof(f1107,plain,
    ( ! [X2,X0,X1] :
        ( ~ m0(X1,X0,X2)
        | l1(X0,X1)
        | ~ p0(X2,X0) )
    | ~ spl0_209 ),
    inference(avatar_component_clause,[],[f1106]) ).

fof(f1108,plain,
    ( spl0_166
    | spl0_209 ),
    inference(avatar_split_clause,[],[f41,f1106,f952]) ).

fof(f1110,definition,
    ( spl0_210
  <=> ! [X1] :
        ( ~ l0(X1)
        | ~ l1(X1,X1) ) ),
    introduced(definition,[new_symbols(definition,[spl0_210])],[avatar_definition]) ).

fof(f1111,plain,
    ( ! [X1] :
        ( ~ l1(X1,X1)
        | ~ l0(X1) )
    | ~ spl0_210 ),
    inference(avatar_component_clause,[],[f1110]) ).

fof(f1113,definition,
    ( spl0_211
  <=> ! [X0] :
        ( l1(X0,X0)
        | ~ k1(X0) ) ),
    introduced(definition,[new_symbols(definition,[spl0_211])],[avatar_definition]) ).

fof(f1114,plain,
    ( ! [X0] :
        ( l1(X0,X0)
        | ~ k1(X0) )
    | ~ spl0_211 ),
    inference(avatar_component_clause,[],[f1113]) ).

fof(f1115,plain,
    ( spl0_210
    | spl0_211 ),
    inference(avatar_split_clause,[],[f42,f1113,f1110]) ).

fof(f1407,plain,
    ( $false
    | spl0_132 ),
    inference(forward_subsumption_resolution,[],[f829,f1]) ).

fof(f1408,plain,
    spl0_132,
    inference(avatar_contradiction_clause,[],[f1407]) ).

fof(f1411,plain,
    ( $false
    | ~ spl0_166 ),
    inference(resolution,[],[f953,f9]) ).

fof(f1414,plain,
    ~ spl0_166,
    inference(avatar_contradiction_clause,[],[f1411]) ).

fof(f1417,plain,
    ( $false
    | ~ spl0_125 ),
    inference(resolution,[],[f805,f14]) ).

fof(f1418,plain,
    ~ spl0_125,
    inference(avatar_contradiction_clause,[],[f1417]) ).

fof(f1488,plain,
    k1(d),
    inference(resolution,[],[f39,f34]) ).

fof(f1505,plain,
    ( ! [X0] : ~ p0(X0,X0)
    | ~ spl0_94 ),
    inference(forward_subsumption_resolution,[],[f163,f695]) ).

fof(f1506,plain,
    ( spl0_125
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f1505,f694,f804]) ).

fof(f1512,plain,
    ( ! [X0] : s1(X0)
    | ~ spl0_124 ),
    inference(resolution,[],[f801,f17]) ).

fof(f1516,plain,
    ( s1(a)
    | ~ spl0_124 ),
    inference(resolution,[],[f801,f36]) ).

fof(f1519,plain,
    ( $false
    | ~ spl0_124
    | spl0_133 ),
    inference(forward_subsumption_resolution,[],[f1516,f832]) ).

fof(f1520,plain,
    ( ~ spl0_124
    | spl0_133 ),
    inference(avatar_contradiction_clause,[],[f1519]) ).

fof(f1560,plain,
    ( ! [X0,X1] :
        ( ~ n0(X0,X1)
        | ~ l0(X1) )
    | ~ spl0_210 ),
    inference(resolution,[],[f40,f1111]) ).

fof(f1578,plain,
    ( ~ l0(c)
    | ~ spl0_210 ),
    inference(resolution,[],[f1560,f26]) ).

fof(f1586,plain,
    ( $false
    | ~ spl0_210 ),
    inference(forward_subsumption_resolution,[],[f1578,f24]) ).

fof(f1587,plain,
    ~ spl0_210,
    inference(avatar_contradiction_clause,[],[f1586]) ).

fof(f1650,plain,
    ( ! [X2,X3,X0] :
        ( ~ m0(X3,X2,X0)
        | l2(X0,X0) )
    | ~ spl0_124
    | ~ spl0_126 ),
    inference(forward_subsumption_resolution,[],[f808,f1512]) ).

fof(f1693,plain,
    ( ~ l1(d,d)
    | ~ s2(d)
    | ~ spl0_134 ),
    inference(resolution,[],[f224,f837]) ).

fof(f1694,plain,
    ( ~ l1(d,d)
    | ~ spl0_111
    | ~ spl0_134 ),
    inference(forward_subsumption_resolution,[],[f1693,f833]) ).

fof(f1702,plain,
    ( ~ k1(d)
    | ~ spl0_111
    | ~ spl0_134
    | ~ spl0_211 ),
    inference(resolution,[],[f1694,f1114]) ).

fof(f1704,plain,
    ( $false
    | ~ spl0_111
    | ~ spl0_134
    | ~ spl0_211 ),
    inference(forward_subsumption_resolution,[],[f1702,f1488]) ).

fof(f1705,plain,
    ( ~ spl0_111
    | ~ spl0_134
    | ~ spl0_211 ),
    inference(avatar_contradiction_clause,[],[f1704]) ).

fof(f1706,plain,
    ( ! [X0] : k3(X0,X0,X0)
    | ~ spl0_124
    | ~ spl0_135 ),
    inference(forward_subsumption_resolution,[],[f840,f1512]) ).

fof(f1754,plain,
    ( ! [X0] : l2(X0,X0)
    | ~ spl0_124
    | ~ spl0_126 ),
    inference(resolution,[],[f1650,f19]) ).

fof(f2391,plain,
    ( ! [X0,X1] :
        ( l1(d,X0)
        | ~ p0(X1,d) )
    | ~ spl0_209 ),
    inference(resolution,[],[f1107,f19]) ).

fof(f2431,definition,
    ( spl0_323
  <=> ! [X1] : ~ p0(X1,d) ),
    introduced(definition,[new_symbols(definition,[spl0_323])],[avatar_definition]) ).

fof(f2432,plain,
    ( ! [X1] : ~ p0(X1,d)
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f2431]) ).

fof(f2434,definition,
    ( spl0_324
  <=> ! [X0] : l1(d,X0) ),
    introduced(definition,[new_symbols(definition,[spl0_324])],[avatar_definition]) ).

fof(f2435,plain,
    ( ! [X0] : l1(d,X0)
    | ~ spl0_324 ),
    inference(avatar_component_clause,[],[f2434]) ).

fof(f2436,plain,
    ( spl0_323
    | spl0_324
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f2391,f1106,f2434,f2431]) ).

fof(f2452,plain,
    ( ! [X0,X1] :
        ( l2(X0,X1)
        | ~ n0(e,X1)
        | ~ l2(X1,X1) )
    | ~ spl0_124 ),
    inference(forward_subsumption_resolution,[],[f169,f1512]) ).

fof(f2453,plain,
    ( ! [X0,X1] :
        ( l2(X0,X1)
        | ~ n0(e,X1) )
    | ~ spl0_124
    | ~ spl0_126 ),
    inference(forward_subsumption_resolution,[],[f2452,f1754]) ).

fof(f2454,plain,
    ( $false
    | ~ spl0_323 ),
    inference(resolution,[],[f2432,f10]) ).

fof(f2457,plain,
    ~ spl0_323,
    inference(avatar_contradiction_clause,[],[f2454]) ).

fof(f2462,plain,
    ( ~ n0(e,b)
    | ~ spl0_124
    | ~ spl0_126
    | spl0_179 ),
    inference(resolution,[],[f2453,f1000]) ).

fof(f2466,plain,
    ( $false
    | ~ spl0_124
    | ~ spl0_126
    | spl0_179 ),
    inference(forward_subsumption_resolution,[],[f2462,f11]) ).

fof(f2467,plain,
    ( ~ spl0_124
    | ~ spl0_126
    | spl0_179 ),
    inference(avatar_contradiction_clause,[],[f2466]) ).

fof(f3082,plain,
    ( ! [X2,X0,X1] :
        ( ~ k3(X0,X0,X1)
        | ~ q2(b,X2,X1)
        | q4(X1,X2) )
    | ~ spl0_180 ),
    inference(resolution,[],[f333,f1003]) ).

fof(f3528,plain,
    ( ! [X0,X1] :
        ( ~ q2(b,X0,X1)
        | q4(X1,X0) )
    | ~ spl0_124
    | ~ spl0_135
    | ~ spl0_180 ),
    inference(resolution,[],[f3082,f1706]) ).

fof(f4058,plain,
    ( ! [X0] :
        ( q4(X0,b)
        | ~ l1(X0,b) )
    | ~ spl0_124
    | ~ spl0_135
    | ~ spl0_180 ),
    inference(resolution,[],[f3528,f224]) ).

fof(f4132,plain,
    ( ~ l1(d,b)
    | ~ spl0_124
    | ~ spl0_135
    | ~ spl0_180 ),
    inference(resolution,[],[f4058,f369]) ).

fof(f4133,plain,
    ( $false
    | ~ spl0_124
    | ~ spl0_135
    | ~ spl0_180
    | ~ spl0_324 ),
    inference(forward_subsumption_resolution,[],[f4132,f2435]) ).

fof(f4134,plain,
    ( ~ spl0_124
    | ~ spl0_135
    | ~ spl0_180
    | ~ spl0_324 ),
    inference(avatar_contradiction_clause,[],[f4133]) ).

cnf(s59,plain,
    ( spl0_94
    | spl0_124 ),
    inference(sat_conversion,[],[f802]) ).

cnf(s60,plain,
    ( spl0_125
    | spl0_126 ),
    inference(sat_conversion,[],[f809]) ).

cnf(s63,plain,
    ( spl0_111
    | ~ spl0_132
    | ~ spl0_133 ),
    inference(sat_conversion,[],[f834]) ).

cnf(s64,plain,
    ( spl0_134
    | spl0_135 ),
    inference(sat_conversion,[],[f841]) ).

cnf(s92,plain,
    ( ~ spl0_179
    | spl0_180 ),
    inference(sat_conversion,[],[f1004]) ).

cnf(s108,plain,
    ( spl0_166
    | spl0_209 ),
    inference(sat_conversion,[],[f1108]) ).

cnf(s109,plain,
    ( spl0_210
    | spl0_211 ),
    inference(sat_conversion,[],[f1115]) ).

cnf(s162,plain,
    spl0_132,
    inference(sat_conversion,[],[f1408]) ).

cnf(s165,plain,
    ~ spl0_166,
    inference(sat_conversion,[],[f1414]) ).

cnf(s167,plain,
    ~ spl0_125,
    inference(sat_conversion,[],[f1418]) ).

cnf(s206,plain,
    ( ~ spl0_94
    | spl0_125 ),
    inference(sat_conversion,[],[f1506]) ).

cnf(s208,plain,
    ( ~ spl0_124
    | spl0_133 ),
    inference(sat_conversion,[],[f1520]) ).

cnf(s233,plain,
    ~ spl0_210,
    inference(sat_conversion,[],[f1587]) ).

cnf(s259,plain,
    ( ~ spl0_111
    | ~ spl0_134
    | ~ spl0_211 ),
    inference(sat_conversion,[],[f1705]) ).

cnf(s348,plain,
    ( ~ spl0_209
    | spl0_323
    | spl0_324 ),
    inference(sat_conversion,[],[f2436]) ).

cnf(s351,plain,
    ~ spl0_323,
    inference(sat_conversion,[],[f2457]) ).

cnf(s352,plain,
    ( ~ spl0_124
    | ~ spl0_126
    | spl0_179 ),
    inference(sat_conversion,[],[f2467]) ).

cnf(s552,plain,
    ( ~ spl0_124
    | ~ spl0_135
    | ~ spl0_180
    | ~ spl0_324 ),
    inference(sat_conversion,[],[f4134]) ).

cnf(s567,plain,
    ( ~ spl0_209
    | spl0_324 ),
    inference(rat,[],[s348,s351]) ).

cnf(s573,plain,
    ~ spl0_94,
    inference(rat,[],[s206,s167]) ).

cnf(s607,plain,
    spl0_211,
    inference(rat,[],[s109,s233]) ).

cnf(s611,plain,
    spl0_209,
    inference(rat,[],[s108,s165]) ).

cnf(s614,plain,
    spl0_324,
    inference(rat,[],[s567,s611]) ).

cnf(s664,plain,
    ( spl0_111
    | ~ spl0_133 ),
    inference(rat,[],[s63,s162]) ).

cnf(s674,plain,
    spl0_126,
    inference(rat,[],[s60,s167]) ).

cnf(s675,plain,
    spl0_124,
    inference(rat,[],[s59,s573]) ).

cnf(s680,plain,
    spl0_179,
    inference(rat,[],[s352,s674,s675]) ).

cnf(s689,plain,
    spl0_133,
    inference(rat,[],[s208,s675]) ).

cnf(s690,plain,
    spl0_180,
    inference(rat,[],[s92,s680]) ).

cnf(s695,plain,
    spl0_111,
    inference(rat,[],[s664,s689]) ).

cnf(s696,plain,
    ~ spl0_135,
    inference(rat,[],[s552,s614,s675,s690]) ).

cnf(s700,plain,
    ~ spl0_134,
    inference(rat,[],[s259,s607,s695]) ).

cnf(s702,plain,
    $false,
    inference(rat,[],[s64,s696,s700]) ).

fof(f4135,plain,
    $false,
    inference(avatar_sat_refutation,[],[s702]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SYN181-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18  % Computer : n009.cluster.edu
% 0.10/0.18  % Model    : x86_64 x86_64
% 0.10/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18  % Memory   : 8046.5625MB
% 0.10/0.18  % OS       : Linux 6.8.0-71-generic
% 0.10/0.18  % CPULimit : 300
% 0.10/0.18  % WCLimit  : 300
% 0.10/0.18  % DateTime : Mon Sep 28 15:37:45 UTC 2026
% 0.10/0.18  % CPUTime  : 
% 0.10/0.18  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22  Running first-order theorem proving
% 0.10/0.22  Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.83/0.95  % (3162571)Input is clausal, will run a generic CNF schedule.
% 0.83/0.95  % (3162638)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=464130312:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.83/0.95  % (3162638)First to succeed.
% 0.83/0.95  % (3162638)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3162571"
% 0.83/0.95  % (3162636)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=258566582:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.83/0.95  % (3162634)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=797382967:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.83/0.95  % (3162635)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3601097198:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.83/0.95  % (3162637)lrs+10_1_sil=8000:sp=occurrence:random_seed=2925823894:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.83/0.95  % (3162639)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=547671120:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.83/0.95  % (3162640)dis-21_1_sil=8000:lcm=predicate:random_seed=975916258:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.83/0.95  % (3162637)Also succeeded, but the first one will report.
% 0.83/0.95  % (3162639)Also succeeded, but the first one will report.
% 0.83/0.95  % (3162640)Instruction limit reached! 
% 0.83/0.95  % (3162640)------------------------------
% 0.83/0.95  % (3162640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/0.95  % (3162640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.95  % (3162640)CaDiCaL version: 2.1.3
% 0.83/0.95  % (3162640)Termination reason: Instruction limit
% 0.83/0.95  % (3162640)Termination phase: Saturation
% 0.83/0.95  % (3162640)Time elapsed: 0.055 s
% 0.83/0.95  % (3162640)Peak memory usage: 89 MB
% 0.83/0.95  % (3162640)Instructions burned: 119 (million)
% 0.83/0.95  % (3162638)Refutation found. Thanks to Tanya!
% 0.83/0.95  % SZS status Unsatisfiable for theBenchmark
% 0.83/0.95  % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.14  % (3162638)------------------------------
% 2.74/1.14  % (3162638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.14  % (3162638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.14  % (3162638)CaDiCaL version: 2.1.3
% 2.74/1.14  % (3162638)Termination reason: Refutation
% 2.74/1.14  % (3162638)Time elapsed: 0.027 s
% 2.74/1.14  % (3162638)Peak memory usage: 91 MB
% 2.74/1.14  % (3162638)Instructions burned: 73 (million)
% 2.74/1.14  % (3162638)------------------------------
% 2.74/1.14  % (3162638)------------------------------
% 2.74/1.14  % (3162571)Success in time 0.292 s
% 2.74/1.14  % Vampire exiting
%------------------------------------------------------------------------------