TSTP Solution File: SET918+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET918+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 : n007.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 18:22:44 EDT 2022

% Result   : Theorem 1.20s 0.54s
% Output   : Refutation 1.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   36 (  12 unt;   0 def)
%            Number of atoms       :   85 (  30 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   84 (  35   ~;  26   |;  10   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   75 (  72   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f273,plain,
    $false,
    inference(subsumption_resolution,[],[f272,f56]) ).

fof(f56,plain,
    ~ sQ6_eqProxy(sK2,sK4),
    inference(equality_proxy_replacement,[],[f32,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( sQ6_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ6_eqProxy])]) ).

fof(f32,plain,
    sK2 != sK4,
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ? [X2,X0,X1] :
      ( singleton(X1) = set_intersection2(unordered_pair(X1,X2),X0)
      & in(X2,X0)
      & X1 != X2 ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ~ ! [X1,X0,X2] :
        ~ ( singleton(X1) = set_intersection2(unordered_pair(X1,X2),X0)
          & in(X2,X0)
          & X1 != X2 ),
    inference(rectify,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X2,X0,X1] :
        ~ ( singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2)
          & X0 != X1
          & in(X1,X2) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X2,X0,X1] :
      ~ ( singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2)
        & X0 != X1
        & in(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).

fof(f272,plain,
    sQ6_eqProxy(sK2,sK4),
    inference(resolution,[],[f252,f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ sQ6_eqProxy(X0,X1)
      | sQ6_eqProxy(X1,X0) ),
    inference(equality_proxy_axiom,[],[f44]) ).

fof(f252,plain,
    sQ6_eqProxy(sK4,sK2),
    inference(subsumption_resolution,[],[f250,f33]) ).

fof(f33,plain,
    in(sK2,sK3),
    inference(cnf_transformation,[],[f20]) ).

fof(f250,plain,
    ( ~ in(sK2,sK3)
    | sQ6_eqProxy(sK4,sK2) ),
    inference(resolution,[],[f179,f66]) ).

fof(f66,plain,
    ! [X0] : sQ6_eqProxy(X0,X0),
    inference(equality_proxy_axiom,[],[f44]) ).

fof(f179,plain,
    ! [X1] :
      ( ~ sQ6_eqProxy(sK2,X1)
      | sQ6_eqProxy(sK4,X1)
      | ~ in(X1,sK3) ),
    inference(resolution,[],[f172,f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ in(X1,singleton(X0))
      | sQ6_eqProxy(X0,X1) ),
    inference(resolution,[],[f45,f66]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ sQ6_eqProxy(singleton(X1),X0)
      | sQ6_eqProxy(X1,X2)
      | ~ in(X2,X0) ),
    inference(equality_proxy_replacement,[],[f24,f44,f44]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( singleton(X1) != X0
      | X1 = X2
      | ~ in(X2,X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> X1 = X2 )
    <=> singleton(X1) = X0 ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f172,plain,
    ! [X0] :
      ( in(X0,singleton(sK4))
      | ~ sQ6_eqProxy(sK2,X0)
      | ~ in(X0,sK3) ),
    inference(resolution,[],[f71,f122]) ).

fof(f122,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sK4,sK2))
      | in(X0,singleton(sK4))
      | ~ in(X0,sK3) ),
    inference(resolution,[],[f62,f55]) ).

fof(f55,plain,
    sQ6_eqProxy(set_intersection2(unordered_pair(sK4,sK2),sK3),singleton(sK4)),
    inference(equality_proxy_replacement,[],[f34,f44]) ).

fof(f34,plain,
    set_intersection2(unordered_pair(sK4,sK2),sK3) = singleton(sK4),
    inference(cnf_transformation,[],[f20]) ).

fof(f62,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sQ6_eqProxy(set_intersection2(X1,X2),X0)
      | ~ in(X3,X1)
      | in(X3,X0)
      | ~ in(X3,X2) ),
    inference(equality_proxy_replacement,[],[f39,f44]) ).

fof(f39,plain,
    ! [X2,X3,X0,X1] :
      ( set_intersection2(X1,X2) != X0
      | ~ in(X3,X1)
      | ~ in(X3,X2)
      | in(X3,X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( in(X3,X0)
        <=> ( in(X3,X2)
            & in(X3,X1) ) )
    <=> set_intersection2(X1,X2) = X0 ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) )
    <=> set_intersection2(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f71,plain,
    ! [X2,X0,X1] :
      ( in(X0,unordered_pair(X1,X2))
      | ~ sQ6_eqProxy(X2,X0) ),
    inference(resolution,[],[f53,f58]) ).

fof(f58,plain,
    ! [X0,X1] : sQ6_eqProxy(unordered_pair(X0,X1),unordered_pair(X1,X0)),
    inference(equality_proxy_replacement,[],[f36,f44]) ).

fof(f36,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[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(f53,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sQ6_eqProxy(unordered_pair(X2,X0),X1)
      | in(X3,X1)
      | ~ sQ6_eqProxy(X2,X3) ),
    inference(equality_proxy_replacement,[],[f26,f44,f44]) ).

fof(f26,plain,
    ! [X2,X3,X0,X1] :
      ( unordered_pair(X2,X0) != X1
      | in(X3,X1)
      | X2 != X3 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( ( X2 = X3
            | X0 = X3 )
        <=> in(X3,X1) )
    <=> unordered_pair(X2,X0) = X1 ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X2,X0] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.13/0.35  % Computer : n007.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 14:15:01 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.52  % (352)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 1.20/0.52  % (348)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.20/0.52  % (360)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 1.20/0.52  % (343)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)
% 1.20/0.52  % (344)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.20/0.53  % (360)First to succeed.
% 1.20/0.53  % (352)Refutation not found, incomplete strategy% (352)------------------------------
% 1.20/0.53  % (352)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.20/0.53  % (352)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.20/0.53  % (352)Termination reason: Refutation not found, incomplete strategy
% 1.20/0.53  
% 1.20/0.53  % (352)Memory used [KB]: 1407
% 1.20/0.53  % (352)Time elapsed: 0.109 s
% 1.20/0.53  % (352)Instructions burned: 2 (million)
% 1.20/0.53  % (352)------------------------------
% 1.20/0.53  % (352)------------------------------
% 1.20/0.53  % (347)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)
% 1.20/0.54  % (360)Refutation found. Thanks to Tanya!
% 1.20/0.54  % SZS status Theorem for theBenchmark
% 1.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 1.20/0.54  % (360)------------------------------
% 1.20/0.54  % (360)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.20/0.54  % (360)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.20/0.54  % (360)Termination reason: Refutation
% 1.20/0.54  
% 1.20/0.54  % (360)Memory used [KB]: 6012
% 1.20/0.54  % (360)Time elapsed: 0.107 s
% 1.20/0.54  % (360)Instructions burned: 9 (million)
% 1.20/0.54  % (360)------------------------------
% 1.20/0.54  % (360)------------------------------
% 1.20/0.54  % (339)Success in time 0.18 s
%------------------------------------------------------------------------------