TSTP Solution File: SWV381+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWV381+1 : 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_uns --cores 0 -t %d %s

% Computer : n018.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 18:45:23 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   46 (   7 unt;   0 def)
%            Number of atoms       :  113 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  112 (  45   ~;  34   |;  17   &)
%                                         (   5 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :  109 (  95   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f186,plain,
    $false,
    inference(subsumption_resolution,[],[f185,f132]) ).

fof(f132,plain,
    phi(findmin_cpq_eff(triple(sK1,sK0,sK2))),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ( phi(findmin_cpq_eff(triple(sK1,sK0,sK2)))
    & ~ issmallestelement_pq(i(triple(sK1,sK0,sK2)),findmin_cpq_res(triple(sK1,sK0,sK2))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f102,f103]) ).

fof(f103,plain,
    ( ? [X0,X1,X2] :
        ( phi(findmin_cpq_eff(triple(X1,X0,X2)))
        & ~ issmallestelement_pq(i(triple(X1,X0,X2)),findmin_cpq_res(triple(X1,X0,X2))) )
   => ( phi(findmin_cpq_eff(triple(sK1,sK0,sK2)))
      & ~ issmallestelement_pq(i(triple(sK1,sK0,sK2)),findmin_cpq_res(triple(sK1,sK0,sK2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ? [X0,X1,X2] :
      ( phi(findmin_cpq_eff(triple(X1,X0,X2)))
      & ~ issmallestelement_pq(i(triple(X1,X0,X2)),findmin_cpq_res(triple(X1,X0,X2))) ),
    inference(rectify,[],[f89]) ).

fof(f89,plain,
    ? [X1,X2,X0] :
      ( phi(findmin_cpq_eff(triple(X2,X1,X0)))
      & ~ issmallestelement_pq(i(triple(X2,X1,X0)),findmin_cpq_res(triple(X2,X1,X0))) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f67,plain,
    ~ ! [X2,X0,X1] :
        ( phi(findmin_cpq_eff(triple(X2,X1,X0)))
       => issmallestelement_pq(i(triple(X2,X1,X0)),findmin_cpq_res(triple(X2,X1,X0))) ),
    inference(rectify,[],[f66]) ).

fof(f66,negated_conjecture,
    ~ ! [X2,X1,X0] :
        ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
       => issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
    inference(negated_conjecture,[],[f65]) ).

fof(f65,conjecture,
    ! [X2,X1,X0] :
      ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
     => issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_co) ).

fof(f185,plain,
    ~ phi(findmin_cpq_eff(triple(sK1,sK0,sK2))),
    inference(subsumption_resolution,[],[f183,f166]) ).

fof(f166,plain,
    ~ less_than(findmin_cpq_res(triple(sK1,sK0,sK2)),sK3(findmin_cpq_res(triple(sK1,sK0,sK2)),i(triple(sK1,sK0,sK2)))),
    inference(resolution,[],[f131,f145]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( issmallestelement_pq(X1,X0)
      | ~ less_than(X0,sK3(X0,X1)) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ( contains_pq(X1,sK3(X0,X1))
        & ~ less_than(X0,sK3(X0,X1)) )
      | issmallestelement_pq(X1,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f114,f115]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( contains_pq(X1,X2)
          & ~ less_than(X0,X2) )
     => ( contains_pq(X1,sK3(X0,X1))
        & ~ less_than(X0,sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( contains_pq(X1,X2)
          & ~ less_than(X0,X2) )
      | issmallestelement_pq(X1,X0) ),
    inference(rectify,[],[f93]) ).

fof(f93,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( contains_pq(X0,X2)
          & ~ less_than(X1,X2) )
      | issmallestelement_pq(X0,X1) ),
    inference(ennf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( contains_pq(X0,X2)
         => less_than(X1,X2) )
     => issmallestelement_pq(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f10]) ).

fof(f10,axiom,
    ! [X1,X0] :
      ( issmallestelement_pq(X0,X1)
    <=> ! [X2] :
          ( contains_pq(X0,X2)
         => less_than(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).

fof(f131,plain,
    ~ issmallestelement_pq(i(triple(sK1,sK0,sK2)),findmin_cpq_res(triple(sK1,sK0,sK2))),
    inference(cnf_transformation,[],[f104]) ).

fof(f183,plain,
    ( less_than(findmin_cpq_res(triple(sK1,sK0,sK2)),sK3(findmin_cpq_res(triple(sK1,sK0,sK2)),i(triple(sK1,sK0,sK2))))
    | ~ phi(findmin_cpq_eff(triple(sK1,sK0,sK2))) ),
    inference(resolution,[],[f178,f174]) ).

fof(f174,plain,
    ! [X2,X3,X0,X1] :
      ( ~ contains_cpq(triple(X0,X1,X2),X3)
      | less_than(findmin_cpq_res(triple(X0,X1,X2)),X3)
      | ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
    inference(subsumption_resolution,[],[f172,f144]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( less_than(X0,X1)
      | less_than(X1,X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    inference(rectify,[],[f74]) ).

fof(f74,plain,
    ! [X1,X0] :
      ( less_than(X0,X1)
      | less_than(X1,X0) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( less_than(X0,X1)
      | less_than(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).

fof(f172,plain,
    ! [X2,X3,X0,X1] :
      ( less_than(findmin_cpq_res(triple(X0,X1,X2)),X3)
      | ~ contains_cpq(triple(X0,X1,X2),X3)
      | ~ less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
      | ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
    inference(resolution,[],[f141,f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | strictly_less_than(X0,X1)
      | ~ less_than(X0,X1) ),
    inference(rectify,[],[f99]) ).

fof(f99,plain,
    ! [X1,X0] :
      ( less_than(X0,X1)
      | strictly_less_than(X1,X0)
      | ~ less_than(X1,X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ! [X1,X0] :
      ( strictly_less_than(X1,X0)
      | ~ less_than(X1,X0)
      | less_than(X0,X1) ),
    inference(ennf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X1,X0] :
      ( ( less_than(X1,X0)
        & ~ less_than(X0,X1) )
     => strictly_less_than(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f72]) ).

fof(f72,plain,
    ! [X1,X0] :
      ( ( less_than(X1,X0)
        & ~ less_than(X0,X1) )
    <=> strictly_less_than(X1,X0) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( strictly_less_than(X0,X1)
    <=> ( less_than(X0,X1)
        & ~ less_than(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] :
      ( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1)))
      | ~ phi(findmin_cpq_eff(triple(X0,X2,X1)))
      | ~ contains_cpq(triple(X0,X2,X1),X3) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( ~ phi(findmin_cpq_eff(triple(X0,X2,X1)))
      | ! [X3] :
          ( ~ contains_cpq(triple(X0,X2,X1),X3)
          | ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1))) ) ),
    inference(rectify,[],[f95]) ).

fof(f95,plain,
    ! [X1,X0,X2] :
      ( ~ phi(findmin_cpq_eff(triple(X1,X2,X0)))
      | ! [X3] :
          ( ~ contains_cpq(triple(X1,X2,X0),X3)
          | ~ strictly_less_than(X3,findmin_cpq_res(triple(X1,X2,X0))) ) ),
    inference(ennf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( strictly_less_than(X3,findmin_cpq_res(triple(X1,X2,X0)))
          & contains_cpq(triple(X1,X2,X0),X3) )
     => ~ phi(findmin_cpq_eff(triple(X1,X2,X0))) ),
    inference(rectify,[],[f64]) ).

fof(f64,axiom,
    ! [X2,X0,X1] :
      ( ? [X3] :
          ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
          & contains_cpq(triple(X0,X1,X2),X3) )
     => ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_l18) ).

fof(f178,plain,
    contains_cpq(triple(sK1,sK0,sK2),sK3(findmin_cpq_res(triple(sK1,sK0,sK2)),i(triple(sK1,sK0,sK2)))),
    inference(resolution,[],[f165,f159]) ).

fof(f159,plain,
    ! [X2,X3,X0,X1] :
      ( ~ contains_pq(i(triple(X0,X3,X2)),X1)
      | contains_cpq(triple(X0,X3,X2),X1) ),
    inference(cnf_transformation,[],[f128]) ).

fof(f128,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_pq(i(triple(X0,X3,X2)),X1)
        | ~ contains_cpq(triple(X0,X3,X2),X1) )
      & ( contains_cpq(triple(X0,X3,X2),X1)
        | ~ contains_pq(i(triple(X0,X3,X2)),X1) ) ),
    inference(rectify,[],[f127]) ).

fof(f127,plain,
    ! [X0,X2,X3,X1] :
      ( ( contains_pq(i(triple(X0,X1,X3)),X2)
        | ~ contains_cpq(triple(X0,X1,X3),X2) )
      & ( contains_cpq(triple(X0,X1,X3),X2)
        | ~ contains_pq(i(triple(X0,X1,X3)),X2) ) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X2,X3,X1] :
      ( contains_pq(i(triple(X0,X1,X3)),X2)
    <=> contains_cpq(triple(X0,X1,X3),X2) ),
    inference(rectify,[],[f63]) ).

fof(f63,axiom,
    ! [X0,X1,X3,X2] :
      ( contains_pq(i(triple(X0,X1,X2)),X3)
    <=> contains_cpq(triple(X0,X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_li56) ).

fof(f165,plain,
    contains_pq(i(triple(sK1,sK0,sK2)),sK3(findmin_cpq_res(triple(sK1,sK0,sK2)),i(triple(sK1,sK0,sK2)))),
    inference(resolution,[],[f131,f146]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( issmallestelement_pq(X1,X0)
      | contains_pq(X1,sK3(X0,X1)) ),
    inference(cnf_transformation,[],[f116]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWV381+1 : TPTP v8.1.0. Released v3.3.0.
% 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
% 0.13/0.34  % Computer : n018.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 19:24:55 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  % (25565)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.47  % (25544)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)
% 0.19/0.48  % (25557)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.48  % (25544)First to succeed.
% 0.19/0.49  % (25544)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (25544)------------------------------
% 0.19/0.49  % (25544)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (25544)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (25544)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (25544)Memory used [KB]: 1535
% 0.19/0.49  % (25544)Time elapsed: 0.101 s
% 0.19/0.49  % (25544)Instructions burned: 3 (million)
% 0.19/0.49  % (25544)------------------------------
% 0.19/0.49  % (25544)------------------------------
% 0.19/0.49  % (25538)Success in time 0.145 s
%------------------------------------------------------------------------------