TSTP Solution File: SET979+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET979+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Tue May 21 03:25:00 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   17 (   8 unt;   0 def)
%            Number of atoms       :   28 (  27 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   29 (  18   ~;   7   |;   3   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   25 (  19   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f60,plain,
    $false,
    inference(trivial_inequality_removal,[],[f59]) ).

fof(f59,plain,
    cartesian_product2(unordered_pair(sK0,sK1),sK2) != cartesian_product2(unordered_pair(sK0,sK1),sK2),
    inference(forward_demodulation,[],[f53,f26]) ).

fof(f26,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_enumset1) ).

fof(f53,plain,
    cartesian_product2(unordered_pair(sK0,sK1),sK2) != cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2),
    inference(superposition,[],[f35,f29]) ).

fof(f29,plain,
    ! [X2,X0,X1] : cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
      & cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).

fof(f35,plain,
    cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)),
    inference(trivial_inequality_removal,[],[f34]) ).

fof(f34,plain,
    ( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != cartesian_product2(sK2,unordered_pair(sK0,sK1))
    | cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
    inference(forward_demodulation,[],[f33,f26]) ).

fof(f33,plain,
    ( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != cartesian_product2(sK2,set_union2(singleton(sK0),singleton(sK1)))
    | cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
    inference(backward_demodulation,[],[f22,f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] : cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
    inference(cnf_transformation,[],[f8]) ).

fof(f22,plain,
    ( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
    | cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
    | cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f16]) ).

fof(f16,plain,
    ( ? [X0,X1,X2] :
        ( cartesian_product2(X2,unordered_pair(X0,X1)) != set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
        | cartesian_product2(unordered_pair(X0,X1),X2) != set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) )
   => ( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
      | cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1,X2] :
      ( cartesian_product2(X2,unordered_pair(X0,X1)) != set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
      | cartesian_product2(unordered_pair(X0,X1),X2) != set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
        & cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1,X2] :
      ( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
      & cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET979+1 : TPTP v8.2.0. Released v3.2.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n010.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
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 20 11:24:08 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (14474)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (14481)WARNING: value z3 for option sas not known
% 0.14/0.38  % (14480)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  % (14479)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (14481)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  % (14482)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (14485)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  % (14484)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  % (14483)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  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  % (14484)First to succeed.
% 0.14/0.38  TRYING [1]
% 0.14/0.38  % (14484)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14474"
% 0.14/0.38  % (14483)Also succeeded, but the first one will report.
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  % (14484)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (14484)------------------------------
% 0.14/0.38  % (14484)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (14484)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (14484)Memory used [KB]: 774
% 0.14/0.38  % (14484)Time elapsed: 0.004 s
% 0.14/0.38  % (14484)Instructions burned: 5 (million)
% 0.14/0.38  % (14474)Success in time 0.023 s
%------------------------------------------------------------------------------