TSTP Solution File: SET930+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET930+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_uns --cores 0 -t %d %s

% Computer : n023.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 18:22:46 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   53 (  12 unt;   0 def)
%            Number of atoms       :  171 (  84 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  221 ( 103   ~;  58   |;  51   &)
%                                         (   8 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   84 (  75   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f607,plain,
    $false,
    inference(avatar_sat_refutation,[],[f173,f228,f536,f605]) ).

fof(f605,plain,
    ( ~ spl5_3
    | spl5_1 ),
    inference(avatar_split_clause,[],[f591,f120,f128]) ).

fof(f128,plain,
    ( spl5_3
  <=> in(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f120,plain,
    ( spl5_1
  <=> in(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f591,plain,
    ( in(sK1,sK2)
    | ~ in(sK0,sK2) ),
    inference(trivial_inequality_removal,[],[f550]) ).

fof(f550,plain,
    ( ~ in(sK0,sK2)
    | singleton(sK1) != singleton(sK1)
    | in(sK1,sK2) ),
    inference(superposition,[],[f56,f143]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( singleton(X0) = set_difference(unordered_pair(X1,X0),X2)
      | ~ in(X1,X2)
      | in(X0,X2) ),
    inference(superposition,[],[f35,f51]) ).

fof(f51,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
      | ~ in(X1,X2)
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( ( ( in(X1,X2)
            | X0 = X1 )
          & ~ in(X0,X2) )
        | set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
      & ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
        | ( ~ in(X1,X2)
          & X0 != X1 )
        | in(X0,X2) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0,X2] :
      ( ( ( ( in(X0,X2)
            | X0 = X1 )
          & ~ in(X1,X2) )
        | singleton(X1) != set_difference(unordered_pair(X1,X0),X2) )
      & ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
        | ( ~ in(X0,X2)
          & X0 != X1 )
        | in(X1,X2) ) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0,X2] :
      ( ( ( ( in(X0,X2)
            | X0 = X1 )
          & ~ in(X1,X2) )
        | singleton(X1) != set_difference(unordered_pair(X1,X0),X2) )
      & ( singleton(X1) = set_difference(unordered_pair(X1,X0),X2)
        | ( ~ in(X0,X2)
          & X0 != X1 )
        | in(X1,X2) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0,X2] :
      ( ( ( in(X0,X2)
          | X0 = X1 )
        & ~ in(X1,X2) )
    <=> singleton(X1) = set_difference(unordered_pair(X1,X0),X2) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0,X2] :
      ( ( ~ in(X0,X2)
        & ( X0 = X1
          | in(X1,X2) ) )
    <=> set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).

fof(f56,plain,
    set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK1),
    inference(backward_demodulation,[],[f40,f51]) ).

fof(f40,plain,
    set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK1),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK0)
    & empty_set != set_difference(unordered_pair(sK1,sK0),sK2)
    & set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK1)
    & set_difference(unordered_pair(sK1,sK0),sK2) != unordered_pair(sK1,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21]) ).

fof(f21,plain,
    ( ? [X0,X1,X2] :
        ( singleton(X0) != set_difference(unordered_pair(X1,X0),X2)
        & empty_set != set_difference(unordered_pair(X1,X0),X2)
        & singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
        & unordered_pair(X1,X0) != set_difference(unordered_pair(X1,X0),X2) )
   => ( set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK0)
      & empty_set != set_difference(unordered_pair(sK1,sK0),sK2)
      & set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK1)
      & set_difference(unordered_pair(sK1,sK0),sK2) != unordered_pair(sK1,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2] :
      ( singleton(X0) != set_difference(unordered_pair(X1,X0),X2)
      & empty_set != set_difference(unordered_pair(X1,X0),X2)
      & singleton(X1) != set_difference(unordered_pair(X1,X0),X2)
      & unordered_pair(X1,X0) != set_difference(unordered_pair(X1,X0),X2) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ? [X2,X1,X0] :
      ( singleton(X2) != set_difference(unordered_pair(X1,X2),X0)
      & empty_set != set_difference(unordered_pair(X1,X2),X0)
      & singleton(X1) != set_difference(unordered_pair(X1,X2),X0)
      & set_difference(unordered_pair(X1,X2),X0) != unordered_pair(X1,X2) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X2,X0,X1] :
        ~ ( singleton(X2) != set_difference(unordered_pair(X1,X2),X0)
          & empty_set != set_difference(unordered_pair(X1,X2),X0)
          & singleton(X1) != set_difference(unordered_pair(X1,X2),X0)
          & set_difference(unordered_pair(X1,X2),X0) != unordered_pair(X1,X2) ),
    inference(rectify,[],[f10]) ).

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

fof(f9,conjecture,
    ! [X2,X0,X1] :
      ~ ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
        & empty_set != set_difference(unordered_pair(X0,X1),X2)
        & unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).

fof(f536,plain,
    ( ~ spl5_1
    | ~ spl5_3 ),
    inference(avatar_split_clause,[],[f535,f128,f120]) ).

fof(f535,plain,
    ( ~ in(sK0,sK2)
    | ~ in(sK1,sK2) ),
    inference(trivial_inequality_removal,[],[f492]) ).

fof(f492,plain,
    ( empty_set != empty_set
    | ~ in(sK0,sK2)
    | ~ in(sK1,sK2) ),
    inference(superposition,[],[f57,f96]) ).

fof(f96,plain,
    ! [X3,X4,X5] :
      ( empty_set = set_difference(unordered_pair(X4,X3),X5)
      | ~ in(X3,X5)
      | ~ in(X4,X5) ),
    inference(superposition,[],[f45,f51]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( empty_set = set_difference(unordered_pair(X0,X1),X2)
      | ~ in(X1,X2)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
        | ~ in(X0,X2)
        | ~ in(X1,X2) )
      & ( ( in(X0,X2)
          & in(X1,X2) )
        | empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( ( empty_set = set_difference(unordered_pair(X2,X0),X1)
        | ~ in(X2,X1)
        | ~ in(X0,X1) )
      & ( ( in(X2,X1)
          & in(X0,X1) )
        | empty_set != set_difference(unordered_pair(X2,X0),X1) ) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X2,X0,X1] :
      ( ( empty_set = set_difference(unordered_pair(X2,X0),X1)
        | ~ in(X2,X1)
        | ~ in(X0,X1) )
      & ( ( in(X2,X1)
          & in(X0,X1) )
        | empty_set != set_difference(unordered_pair(X2,X0),X1) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X2,X0,X1] :
      ( empty_set = set_difference(unordered_pair(X2,X0),X1)
    <=> ( in(X2,X1)
        & in(X0,X1) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X2,X0] :
      ( ( in(X0,X2)
        & in(X1,X2) )
    <=> empty_set = set_difference(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).

fof(f57,plain,
    empty_set != set_difference(unordered_pair(sK0,sK1),sK2),
    inference(backward_demodulation,[],[f41,f51]) ).

fof(f41,plain,
    empty_set != set_difference(unordered_pair(sK1,sK0),sK2),
    inference(cnf_transformation,[],[f22]) ).

fof(f228,plain,
    ( spl5_3
    | spl5_1 ),
    inference(avatar_split_clause,[],[f211,f120,f128]) ).

fof(f211,plain,
    ( in(sK1,sK2)
    | in(sK0,sK2) ),
    inference(trivial_inequality_removal,[],[f190]) ).

fof(f190,plain,
    ( in(sK0,sK2)
    | in(sK1,sK2)
    | unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1) ),
    inference(superposition,[],[f54,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( unordered_pair(X1,X0) = set_difference(unordered_pair(X1,X0),X2)
      | in(X0,X2)
      | in(X1,X2) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( ( ~ in(X1,X2)
          & ~ in(X0,X2) )
        | unordered_pair(X1,X0) != set_difference(unordered_pair(X1,X0),X2) )
      & ( unordered_pair(X1,X0) = set_difference(unordered_pair(X1,X0),X2)
        | in(X1,X2)
        | in(X0,X2) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X0,X2,X1] :
      ( ( ( ~ in(X2,X1)
          & ~ in(X0,X1) )
        | unordered_pair(X2,X0) != set_difference(unordered_pair(X2,X0),X1) )
      & ( unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1)
        | in(X2,X1)
        | in(X0,X1) ) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X2,X1] :
      ( ( ( ~ in(X2,X1)
          & ~ in(X0,X1) )
        | unordered_pair(X2,X0) != set_difference(unordered_pair(X2,X0),X1) )
      & ( unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1)
        | in(X2,X1)
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X2,X1] :
      ( ( ~ in(X2,X1)
        & ~ in(X0,X1) )
    <=> unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X2,X0] :
      ( ( ~ in(X0,X2)
        & ~ in(X1,X2) )
    <=> unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).

fof(f54,plain,
    set_difference(unordered_pair(sK0,sK1),sK2) != unordered_pair(sK0,sK1),
    inference(backward_demodulation,[],[f39,f51]) ).

fof(f39,plain,
    set_difference(unordered_pair(sK1,sK0),sK2) != unordered_pair(sK1,sK0),
    inference(cnf_transformation,[],[f22]) ).

fof(f173,plain,
    ( ~ spl5_1
    | spl5_3 ),
    inference(avatar_split_clause,[],[f162,f128,f120]) ).

fof(f162,plain,
    ( in(sK0,sK2)
    | ~ in(sK1,sK2) ),
    inference(trivial_inequality_removal,[],[f148]) ).

fof(f148,plain,
    ( ~ in(sK1,sK2)
    | singleton(sK0) != singleton(sK0)
    | in(sK0,sK2) ),
    inference(superposition,[],[f55,f35]) ).

fof(f55,plain,
    set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0),
    inference(backward_demodulation,[],[f42,f51]) ).

fof(f42,plain,
    set_difference(unordered_pair(sK1,sK0),sK2) != singleton(sK0),
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % 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 : n023.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 14:52:20 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (12197)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (12205)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50  % (12197)Instruction limit reached!
% 0.19/0.50  % (12197)------------------------------
% 0.19/0.50  % (12197)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (12197)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (12197)Termination reason: Unknown
% 0.19/0.50  % (12197)Termination phase: Saturation
% 0.19/0.50  
% 0.19/0.50  % (12197)Memory used [KB]: 5884
% 0.19/0.50  % (12197)Time elapsed: 0.005 s
% 0.19/0.50  % (12197)Instructions burned: 3 (million)
% 0.19/0.50  % (12197)------------------------------
% 0.19/0.50  % (12197)------------------------------
% 0.19/0.50  % (12189)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (12192)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.51  % (12192)Refutation not found, incomplete strategy% (12192)------------------------------
% 0.19/0.51  % (12192)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (12192)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (12192)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (12192)Memory used [KB]: 5884
% 0.19/0.51  % (12192)Time elapsed: 0.116 s
% 0.19/0.51  % (12192)Instructions burned: 2 (million)
% 0.19/0.51  % (12192)------------------------------
% 0.19/0.51  % (12192)------------------------------
% 0.19/0.51  % (12193)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.51  % (12188)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.51  % (12190)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (12186)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (12186)Refutation not found, incomplete strategy% (12186)------------------------------
% 0.19/0.51  % (12186)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (12186)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (12186)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51  
% 0.19/0.51  % (12186)Memory used [KB]: 5884
% 0.19/0.51  % (12186)Time elapsed: 0.116 s
% 0.19/0.51  % (12186)Instructions burned: 2 (million)
% 0.19/0.51  % (12186)------------------------------
% 0.19/0.51  % (12186)------------------------------
% 0.19/0.51  % (12183)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.52  % (12205)First to succeed.
% 0.19/0.52  % (12189)Also succeeded, but the first one will report.
% 0.19/0.52  % (12205)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (12205)------------------------------
% 0.19/0.52  % (12205)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (12205)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (12205)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (12205)Memory used [KB]: 6140
% 0.19/0.52  % (12205)Time elapsed: 0.071 s
% 0.19/0.52  % (12205)Instructions burned: 14 (million)
% 0.19/0.52  % (12205)------------------------------
% 0.19/0.52  % (12205)------------------------------
% 0.19/0.52  % (12182)Success in time 0.168 s
%------------------------------------------------------------------------------