TSTP Solution File: SEU150+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU150+2 : TPTP v8.1.0. Released v3.3.0.
% 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 : n006.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 18:32:10 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   41 (  15 unt;   0 def)
%            Number of atoms       :  166 ( 116 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  198 (  73   ~;  74   |;  40   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   96 (  80   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f902,plain,
    $false,
    inference(trivial_inequality_removal,[],[f901]) ).

fof(f901,plain,
    sK7 != sK7,
    inference(superposition,[],[f282,f871]) ).

fof(f871,plain,
    sK9 = sK7,
    inference(backward_demodulation,[],[f840,f839]) ).

fof(f839,plain,
    sK8 = sK7,
    inference(resolution,[],[f837,f386]) ).

fof(f386,plain,
    ! [X1,X4] : in(X4,unordered_pair(X4,X1)),
    inference(equality_resolution,[],[f385]) ).

fof(f385,plain,
    ! [X0,X1,X4] :
      ( in(X4,X0)
      | unordered_pair(X4,X1) != X0 ),
    inference(equality_resolution,[],[f305]) ).

fof(f305,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | X2 != X4
      | unordered_pair(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f210]) ).

fof(f210,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X2,X1) = X0
        | ( ( ~ in(sK14(X0,X1,X2),X0)
            | ( sK14(X0,X1,X2) != X2
              & sK14(X0,X1,X2) != X1 ) )
          & ( in(sK14(X0,X1,X2),X0)
            | sK14(X0,X1,X2) = X2
            | sK14(X0,X1,X2) = X1 ) ) )
      & ( ! [X4] :
            ( ( X2 = X4
              | X1 = X4
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ( X2 != X4
                & X1 != X4 ) ) )
        | unordered_pair(X2,X1) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f208,f209]) ).

fof(f209,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ( X2 != X3
              & X1 != X3 ) )
          & ( in(X3,X0)
            | X2 = X3
            | X1 = X3 ) )
     => ( ( ~ in(sK14(X0,X1,X2),X0)
          | ( sK14(X0,X1,X2) != X2
            & sK14(X0,X1,X2) != X1 ) )
        & ( in(sK14(X0,X1,X2),X0)
          | sK14(X0,X1,X2) = X2
          | sK14(X0,X1,X2) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f208,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X2,X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) )
            & ( in(X3,X0)
              | X2 = X3
              | X1 = X3 ) ) )
      & ( ! [X4] :
            ( ( X2 = X4
              | X1 = X4
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ( X2 != X4
                & X1 != X4 ) ) )
        | unordered_pair(X2,X1) != X0 ) ),
    inference(rectify,[],[f207]) ).

fof(f207,plain,
    ! [X0,X2,X1] :
      ( ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) )
            & ( in(X3,X0)
              | X1 = X3
              | X2 = X3 ) ) )
      & ( ! [X3] :
            ( ( X1 = X3
              | X2 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(flattening,[],[f206]) ).

fof(f206,plain,
    ! [X0,X2,X1] :
      ( ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) )
            & ( in(X3,X0)
              | X1 = X3
              | X2 = X3 ) ) )
      & ( ! [X3] :
            ( ( X1 = X3
              | X2 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X2,X1] :
      ( unordered_pair(X1,X2) = X0
    <=> ! [X3] :
          ( ( X1 = X3
            | X2 = X3 )
        <=> in(X3,X0) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( ( X0 = X3
            | X1 = X3 )
        <=> in(X3,X2) )
    <=> unordered_pair(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f837,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sK7,sK9))
      | sK8 = X0 ),
    inference(superposition,[],[f377,f398]) ).

fof(f398,plain,
    unordered_pair(sK7,sK9) = unordered_pair(sK8,sK8),
    inference(forward_demodulation,[],[f356,f252]) ).

fof(f252,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f356,plain,
    unordered_pair(sK9,sK7) = unordered_pair(sK8,sK8),
    inference(definition_unfolding,[],[f281,f336]) ).

fof(f336,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f281,plain,
    unordered_pair(sK9,sK7) = singleton(sK8),
    inference(cnf_transformation,[],[f187]) ).

fof(f187,plain,
    ( sK9 != sK7
    & unordered_pair(sK9,sK7) = singleton(sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f185,f186]) ).

fof(f186,plain,
    ( ? [X0,X1,X2] :
        ( X0 != X2
        & singleton(X1) = unordered_pair(X2,X0) )
   => ( sK9 != sK7
      & unordered_pair(sK9,sK7) = singleton(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f185,plain,
    ? [X0,X1,X2] :
      ( X0 != X2
      & singleton(X1) = unordered_pair(X2,X0) ),
    inference(rectify,[],[f127]) ).

fof(f127,plain,
    ? [X2,X0,X1] :
      ( X1 != X2
      & singleton(X0) = unordered_pair(X1,X2) ),
    inference(ennf_transformation,[],[f74]) ).

fof(f74,negated_conjecture,
    ~ ! [X1,X0,X2] :
        ( singleton(X0) = unordered_pair(X1,X2)
       => X1 = X2 ),
    inference(negated_conjecture,[],[f73]) ).

fof(f73,conjecture,
    ! [X1,X0,X2] :
      ( singleton(X0) = unordered_pair(X1,X2)
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).

fof(f377,plain,
    ! [X3,X1] :
      ( ~ in(X3,unordered_pair(X1,X1))
      | X1 = X3 ),
    inference(equality_resolution,[],[f353]) ).

fof(f353,plain,
    ! [X3,X0,X1] :
      ( X1 = X3
      | ~ in(X3,X0)
      | unordered_pair(X1,X1) != X0 ),
    inference(definition_unfolding,[],[f266,f336]) ).

fof(f266,plain,
    ! [X3,X0,X1] :
      ( X1 = X3
      | ~ in(X3,X0)
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f175]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ( singleton(X1) = X0
        | ( ( sK5(X0,X1) != X1
            | ~ in(sK5(X0,X1),X0) )
          & ( sK5(X0,X1) = X1
            | in(sK5(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X0)
              | X1 != X3 )
            & ( X1 = X3
              | ~ in(X3,X0) ) )
        | singleton(X1) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f173,f174]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X1 != X2
            | ~ in(X2,X0) )
          & ( X1 = X2
            | in(X2,X0) ) )
     => ( ( sK5(X0,X1) != X1
          | ~ in(sK5(X0,X1),X0) )
        & ( sK5(X0,X1) = X1
          | in(sK5(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( ( singleton(X1) = X0
        | ? [X2] :
            ( ( X1 != X2
              | ~ in(X2,X0) )
            & ( X1 = X2
              | in(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X0)
              | X1 != X3 )
            & ( X1 = X3
              | ~ in(X3,X0) ) )
        | singleton(X1) != X0 ) ),
    inference(rectify,[],[f172]) ).

fof(f172,plain,
    ! [X1,X0] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f840,plain,
    sK9 = sK8,
    inference(resolution,[],[f837,f388]) ).

fof(f388,plain,
    ! [X2,X4] : in(X4,unordered_pair(X2,X4)),
    inference(equality_resolution,[],[f387]) ).

fof(f387,plain,
    ! [X2,X0,X4] :
      ( in(X4,X0)
      | unordered_pair(X2,X4) != X0 ),
    inference(equality_resolution,[],[f304]) ).

fof(f304,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | X1 != X4
      | unordered_pair(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f210]) ).

fof(f282,plain,
    sK9 != sK7,
    inference(cnf_transformation,[],[f187]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU150+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:50:09 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (1034)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  % (1028)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51  % (1055)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.51  % (1028)Instruction limit reached!
% 0.20/0.51  % (1028)------------------------------
% 0.20/0.51  % (1028)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (1028)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (1028)Termination reason: Unknown
% 0.20/0.51  % (1028)Termination phase: Preprocessing 1
% 0.20/0.51  
% 0.20/0.51  % (1028)Memory used [KB]: 895
% 0.20/0.51  % (1028)Time elapsed: 0.004 s
% 0.20/0.51  % (1028)Instructions burned: 2 (million)
% 0.20/0.51  % (1028)------------------------------
% 0.20/0.51  % (1028)------------------------------
% 0.20/0.52  % (1045)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.52  % (1025)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52  % (1054)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.52  % (1036)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (1044)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52  % (1025)Instruction limit reached!
% 0.20/0.52  % (1025)------------------------------
% 0.20/0.52  % (1025)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (1025)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (1025)Termination reason: Unknown
% 0.20/0.52  % (1025)Termination phase: Saturation
% 0.20/0.52  
% 0.20/0.52  % (1025)Memory used [KB]: 5628
% 0.20/0.52  % (1025)Time elapsed: 0.112 s
% 0.20/0.52  % (1025)Instructions burned: 7 (million)
% 0.20/0.52  % (1025)------------------------------
% 0.20/0.52  % (1025)------------------------------
% 0.20/0.52  % (1053)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.53  % (1043)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.53  % (1056)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53  % (1010)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.53  % (1034)First to succeed.
% 0.20/0.53  % (1046)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53  % (1034)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (1034)------------------------------
% 0.20/0.54  % (1034)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (1034)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (1034)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (1034)Memory used [KB]: 1407
% 0.20/0.54  % (1034)Time elapsed: 0.118 s
% 0.20/0.54  % (1034)Instructions burned: 25 (million)
% 0.20/0.54  % (1034)------------------------------
% 0.20/0.54  % (1034)------------------------------
% 0.20/0.54  % (1009)Success in time 0.178 s
%------------------------------------------------------------------------------