%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : n010.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 18:18:25 EDT 2022

% Result   : Unsatisfiable 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   60 (  11 unt;   0 def)
%            Number of atoms       :  125 (  42 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  122 (  57   ~;  61   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   12 (  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f136,plain,
    $false,
    inference(avatar_sat_refutation,[],[f22,f46,f76,f98,f133]) ).

fof(f133,plain,
    ( ~ spl0_1
    | spl0_2 ),
    inference(avatar_contradiction_clause,[],[f132]) ).

fof(f132,plain,
    ( $false
    | ~ spl0_1
    | spl0_2 ),
    inference(trivial_inequality_removal,[],[f126]) ).

fof(f126,plain,
    ( singleton_set(m1) != singleton_set(m1)
    | ~ spl0_1
    | spl0_2 ),
    inference(backward_demodulation,[],[f112,f122]) ).

fof(f122,plain,
    ( m1 = r1
    | ~ spl0_1 ),
    inference(resolution,[],[f118,f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(X0,singleton_set(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_2) ).

fof(f118,plain,
    ( member(m1,singleton_set(r1))
    | ~ spl0_1 ),
    inference(backward_demodulation,[],[f105,f110]) ).

fof(f110,plain,
    ( r1 = m2
    | ~ spl0_1 ),
    inference(resolution,[],[f104,f2]) ).

fof(f104,plain,
    ( member(r1,singleton_set(m2))
    | ~ spl0_1 ),
    inference(superposition,[],[f4,f17]) ).

fof(f17,plain,
    ( unordered_pair(m1,r1) = singleton_set(m2)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f15]) ).

fof(f15,plain,
    ( spl0_1
  <=> unordered_pair(m1,r1) = singleton_set(m2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f4,axiom,
    ! [X0,X1] : member(X1,unordered_pair(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_2) ).

fof(f105,plain,
    ( member(m1,singleton_set(m2))
    | ~ spl0_1 ),
    inference(superposition,[],[f3,f17]) ).

fof(f3,axiom,
    ! [X0,X1] : member(X0,unordered_pair(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_1) ).

fof(f112,plain,
    ( singleton_set(r1) != singleton_set(m1)
    | ~ spl0_1
    | spl0_2 ),
    inference(backward_demodulation,[],[f20,f110]) ).

fof(f20,plain,
    ( singleton_set(m1) != singleton_set(m2)
    | spl0_2 ),
    inference(avatar_component_clause,[],[f19]) ).

fof(f19,plain,
    ( spl0_2
  <=> singleton_set(m1) = singleton_set(m2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f98,plain,
    ~ spl0_4,
    inference(avatar_contradiction_clause,[],[f97]) ).

fof(f97,plain,
    ( $false
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f96,f87]) ).

fof(f87,plain,
    ( m1 != r1
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f8,f84]) ).

fof(f84,plain,
    ( m1 = r2
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f83,f8]) ).

fof(f83,plain,
    ( r1 = r2
    | m1 = r2
    | ~ spl0_4 ),
    inference(resolution,[],[f80,f5]) ).

fof(f5,axiom,
    ! [X2,X0,X1] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_3) ).

fof(f80,plain,
    ( member(r2,unordered_pair(m1,r1))
    | ~ spl0_4 ),
    inference(superposition,[],[f4,f45]) ).

fof(f45,plain,
    ( unordered_pair(m1,r2) = unordered_pair(m1,r1)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f43,plain,
    ( spl0_4
  <=> unordered_pair(m1,r2) = unordered_pair(m1,r1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f8,axiom,
    r1 != r2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).

fof(f96,plain,
    ( m1 = r1
    | ~ spl0_4 ),
    inference(duplicate_literal_removal,[],[f95]) ).

fof(f95,plain,
    ( m1 = r1
    | m1 = r1
    | ~ spl0_4 ),
    inference(resolution,[],[f92,f5]) ).

fof(f92,plain,
    ( member(r1,unordered_pair(m1,m1))
    | ~ spl0_4 ),
    inference(superposition,[],[f4,f88]) ).

fof(f88,plain,
    ( unordered_pair(m1,r1) = unordered_pair(m1,m1)
    | ~ spl0_4 ),
    inference(backward_demodulation,[],[f45,f84]) ).

fof(f76,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f75]) ).

fof(f75,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f74,f66]) ).

fof(f66,plain,
    ( m1 != r1
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f8,f63]) ).

fof(f63,plain,
    ( m1 = r2
    | ~ spl0_3 ),
    inference(resolution,[],[f55,f2]) ).

fof(f55,plain,
    ( member(r2,singleton_set(m1))
    | ~ spl0_3 ),
    inference(superposition,[],[f4,f41]) ).

fof(f41,plain,
    ( unordered_pair(m1,r2) = singleton_set(m1)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f39,plain,
    ( spl0_3
  <=> unordered_pair(m1,r2) = singleton_set(m1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f74,plain,
    ( m1 = r1
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(resolution,[],[f67,f2]) ).

fof(f67,plain,
    ( member(r1,singleton_set(m1))
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(superposition,[],[f4,f59]) ).

fof(f59,plain,
    ( unordered_pair(m1,r1) = singleton_set(m1)
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(duplicate_literal_removal,[],[f58]) ).

fof(f58,plain,
    ( unordered_pair(m1,r1) = singleton_set(m1)
    | unordered_pair(m1,r1) = singleton_set(m1)
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(resolution,[],[f52,f5]) ).

fof(f52,plain,
    ( member(unordered_pair(m1,r1),unordered_pair(singleton_set(m1),singleton_set(m1)))
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(superposition,[],[f4,f49]) ).

fof(f49,plain,
    ( unordered_pair(singleton_set(m1),singleton_set(m1)) = unordered_pair(singleton_set(m1),unordered_pair(m1,r1))
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f34,f41]) ).

fof(f34,plain,
    ( unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m1),unordered_pair(m1,r2))
    | ~ spl0_2 ),
    inference(backward_demodulation,[],[f25,f31]) ).

fof(f31,plain,
    ( m1 = m2
    | ~ spl0_2 ),
    inference(resolution,[],[f30,f2]) ).

fof(f30,plain,
    ( member(m2,singleton_set(m1))
    | ~ spl0_2 ),
    inference(superposition,[],[f1,f21]) ).

fof(f21,plain,
    ( singleton_set(m1) = singleton_set(m2)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f19]) ).

fof(f1,axiom,
    ! [X0] : member(X0,singleton_set(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_1) ).

fof(f25,plain,
    ( unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m1),unordered_pair(m2,r2))
    | ~ spl0_2 ),
    inference(backward_demodulation,[],[f9,f21]) ).

fof(f9,plain,
    unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
    inference(definition_unfolding,[],[f7,f6,f6]) ).

fof(f6,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).

fof(f7,axiom,
    ordered_pair(m1,r1) = ordered_pair(m2,r2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pairs) ).

fof(f46,plain,
    ( spl0_3
    | spl0_4
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f37,f19,f43,f39]) ).

fof(f37,plain,
    ( unordered_pair(m1,r2) = unordered_pair(m1,r1)
    | unordered_pair(m1,r2) = singleton_set(m1)
    | ~ spl0_2 ),
    inference(resolution,[],[f36,f5]) ).

fof(f36,plain,
    ( member(unordered_pair(m1,r2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1)))
    | ~ spl0_2 ),
    inference(backward_demodulation,[],[f10,f31]) ).

fof(f10,plain,
    member(unordered_pair(m2,r2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
    inference(superposition,[],[f4,f9]) ).

fof(f22,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f13,f19,f15]) ).

fof(f13,plain,
    ( singleton_set(m1) = singleton_set(m2)
    | unordered_pair(m1,r1) = singleton_set(m2) ),
    inference(resolution,[],[f11,f5]) ).

fof(f11,plain,
    member(singleton_set(m2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
    inference(superposition,[],[f3,f9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n010.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   : Tue Aug 30 12:55:14 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.51  % (466)lrs+3_8:1_anc=none:erd=off:fsd=on:s2a=on:s2agt=16:sgt=16:sos=on:sp=frequency:ss=included:i=71:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/71Mi)
% 0.19/0.51  % (468)lrs+10_1:1_sos=all:ss=axioms:st=1.5:i=20:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/20Mi)
% 0.19/0.52  % (468)First to succeed.
% 0.19/0.53  % (466)Also succeeded, but the first one will report.
% 0.19/0.53  % (468)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (468)------------------------------
% 0.19/0.53  % (468)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (468)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (468)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (468)Memory used [KB]: 5884
% 0.19/0.53  % (468)Time elapsed: 0.052 s
% 0.19/0.53  % (468)Instructions burned: 6 (million)
% 0.19/0.53  % (468)------------------------------
% 0.19/0.53  % (468)------------------------------
% 0.19/0.53  % (438)Success in time 0.177 s
%------------------------------------------------------------------------------