%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n002.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 18:26:01 EDT 2022

% Result   : Theorem 0.20s 0.48s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (  16 unt;   0 def)
%            Number of atoms       :   44 (  25 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   32 (  17   ~;   5   |;   5   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   42 (  33   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f48,plain,
    $false,
    inference(trivial_inequality_removal,[],[f47]) ).

fof(f47,plain,
    unordered_pair(sK1,sK1) != unordered_pair(sK1,sK1),
    inference(backward_demodulation,[],[f40,f42]) ).

fof(f42,plain,
    sK1 = sK3,
    inference(resolution,[],[f37,f39]) ).

fof(f39,plain,
    subset(unordered_pair(sK1,sK3),unordered_pair(sK1,sK1)),
    inference(backward_demodulation,[],[f34,f35]) ).

fof(f35,plain,
    sK1 = sK2,
    inference(resolution,[],[f32,f34]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( ~ subset(unordered_pair(X1,X2),unordered_pair(X0,X0))
      | X0 = X1 ),
    inference(definition_unfolding,[],[f29,f22]) ).

fof(f22,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( X0 = X1
      | ~ subset(unordered_pair(X1,X2),singleton(X0)) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | ~ subset(unordered_pair(X1,X2),singleton(X0)) ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | ~ subset(unordered_pair(X0,X1),singleton(X2)) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X2,X0] :
      ( subset(unordered_pair(X0,X1),singleton(X2))
     => X0 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).

fof(f34,plain,
    subset(unordered_pair(sK1,sK3),unordered_pair(sK2,sK2)),
    inference(forward_demodulation,[],[f31,f23]) ).

fof(f23,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f31,plain,
    subset(unordered_pair(sK3,sK1),unordered_pair(sK2,sK2)),
    inference(definition_unfolding,[],[f25,f22]) ).

fof(f25,plain,
    subset(unordered_pair(sK3,sK1),singleton(sK2)),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( singleton(sK2) != unordered_pair(sK3,sK1)
    & subset(unordered_pair(sK3,sK1),singleton(sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f15,f16]) ).

fof(f16,plain,
    ( ? [X0,X1,X2] :
        ( singleton(X1) != unordered_pair(X2,X0)
        & subset(unordered_pair(X2,X0),singleton(X1)) )
   => ( singleton(sK2) != unordered_pair(sK3,sK1)
      & subset(unordered_pair(sK3,sK1),singleton(sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( singleton(X1) != unordered_pair(X2,X0)
      & subset(unordered_pair(X2,X0),singleton(X1)) ),
    inference(rectify,[],[f12]) ).

fof(f12,plain,
    ? [X2,X0,X1] :
      ( singleton(X0) != unordered_pair(X1,X2)
      & subset(unordered_pair(X1,X2),singleton(X0)) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ~ ! [X2,X1,X0] :
        ( subset(unordered_pair(X1,X2),singleton(X0))
       => singleton(X0) = unordered_pair(X1,X2) ),
    inference(rectify,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ! [X2,X0,X1] :
        ( subset(unordered_pair(X0,X1),singleton(X2))
       => unordered_pair(X0,X1) = singleton(X2) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ! [X2,X0,X1] :
      ( subset(unordered_pair(X0,X1),singleton(X2))
     => unordered_pair(X0,X1) = singleton(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( ~ subset(unordered_pair(X1,X0),unordered_pair(X2,X2))
      | X0 = X2 ),
    inference(superposition,[],[f32,f23]) ).

fof(f40,plain,
    unordered_pair(sK1,sK3) != unordered_pair(sK1,sK1),
    inference(backward_demodulation,[],[f33,f35]) ).

fof(f33,plain,
    unordered_pair(sK1,sK3) != unordered_pair(sK2,sK2),
    inference(backward_demodulation,[],[f30,f23]) ).

fof(f30,plain,
    unordered_pair(sK2,sK2) != unordered_pair(sK3,sK1),
    inference(definition_unfolding,[],[f26,f22]) ).

fof(f26,plain,
    singleton(sK2) != unordered_pair(sK3,sK1),
    inference(cnf_transformation,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n002.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 14:40:44 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  % (6802)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/48Mi)
% 0.20/0.48  % (6818)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/138Mi)
% 0.20/0.48  % (6818)First to succeed.
% 0.20/0.48  % (6818)Refutation found. Thanks to Tanya!
% 0.20/0.48  % SZS status Theorem for theBenchmark
% 0.20/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.48  % (6818)------------------------------
% 0.20/0.48  % (6818)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (6818)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (6818)Termination reason: Refutation
% 0.20/0.48  
% 0.20/0.48  % (6818)Memory used [KB]: 5373
% 0.20/0.48  % (6818)Time elapsed: 0.080 s
% 0.20/0.48  % (6818)Instructions burned: 2 (million)
% 0.20/0.48  % (6818)------------------------------
% 0.20/0.48  % (6818)------------------------------
% 0.20/0.48  % (6796)Success in time 0.129 s
%------------------------------------------------------------------------------