TSTP Solution File: SWV372+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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 Apr 30 16:46:36 EDT 2024

% Result   : Theorem 0.21s 0.47s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   65 (   9 unt;   0 def)
%            Number of atoms       :  147 (  27 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  139 (  57   ~;  51   |;   9   &)
%                                         (  10 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   5 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :  145 ( 139   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1764,plain,
    $false,
    inference(avatar_sat_refutation,[],[f352,f1490,f1742,f1763]) ).

fof(f1763,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f1762]) ).

fof(f1762,plain,
    ( $false
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f1761,f175]) ).

fof(f175,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(true_and_false_elimination,[],[f40]) ).

fof(f40,axiom,
    ! [X0,X1] :
      ( ok(triple(X0,X1,bad))
    <=> $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).

fof(f1761,plain,
    ( ok(triple(sK0,create_slb,bad))
    | ~ spl5_1 ),
    inference(resolution,[],[f1755,f140]) ).

fof(f140,plain,
    ! [X2,X0,X1] :
      ( ~ phi(triple(X0,X1,X2))
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ~ phi(triple(X0,X1,X2))
      | ok(triple(X0,X1,X2)) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,axiom,
    ! [X0,X1,X2] :
      ( ~ ok(triple(X0,X1,X2))
     => ~ phi(triple(X0,X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l8_lX) ).

fof(f1755,plain,
    ( phi(triple(sK0,create_slb,bad))
    | ~ spl5_1 ),
    inference(forward_demodulation,[],[f1743,f164]) ).

fof(f164,plain,
    ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).

fof(f1743,plain,
    ( phi(findmin_cpq_eff(triple(sK0,create_slb,sK2)))
    | ~ spl5_1 ),
    inference(superposition,[],[f138,f347]) ).

fof(f347,plain,
    ( create_slb = sK1
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f345]) ).

fof(f345,plain,
    ( spl5_1
  <=> create_slb = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f138,plain,
    phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ( ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
    & phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f78,f121]) ).

fof(f121,plain,
    ( ? [X0,X1,X2] :
        ( ~ contains_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
        & phi(findmin_cpq_eff(triple(X0,X1,X2))) )
   => ( ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
      & phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ? [X0,X1,X2] :
      ( ~ contains_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
      & phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
    inference(ennf_transformation,[],[f67]) ).

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

fof(f66,conjecture,
    ! [X0,X1,X2] :
      ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
     => contains_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l8_co) ).

fof(f1742,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_contradiction_clause,[],[f1738]) ).

fof(f1738,plain,
    ( $false
    | spl5_1
    | spl5_2 ),
    inference(resolution,[],[f1735,f138]) ).

fof(f1735,plain,
    ( ! [X0] : ~ phi(findmin_cpq_eff(triple(sK0,sK1,X0)))
    | spl5_1
    | spl5_2 ),
    inference(subsumption_resolution,[],[f1712,f175]) ).

fof(f1712,plain,
    ( ! [X0] :
        ( ~ phi(findmin_cpq_eff(triple(sK0,sK1,X0)))
        | ok(triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad)) )
    | spl5_1
    | spl5_2 ),
    inference(superposition,[],[f140,f1699]) ).

fof(f1699,plain,
    ( ! [X0] : findmin_cpq_eff(triple(sK0,sK1,X0)) = triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad)
    | spl5_1
    | spl5_2 ),
    inference(subsumption_resolution,[],[f1698,f346]) ).

fof(f346,plain,
    ( create_slb != sK1
    | spl5_1 ),
    inference(avatar_component_clause,[],[f345]) ).

fof(f1698,plain,
    ( ! [X0] :
        ( findmin_cpq_eff(triple(sK0,sK1,X0)) = triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad)
        | create_slb = sK1 )
    | spl5_2 ),
    inference(resolution,[],[f195,f441]) ).

fof(f441,plain,
    ( ~ contains_slb(sK1,findmin_pqp_res(sK0))
    | spl5_2 ),
    inference(resolution,[],[f433,f201]) ).

fof(f201,plain,
    ! [X2,X3,X0,X1] :
      ( contains_cpq(triple(X0,X1,X2),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_slb(X1,X3) )
      & ( contains_slb(X1,X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_cpq(triple(X0,X1,X2),X3)
    <=> contains_slb(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f433,plain,
    ( ~ contains_cpq(triple(sK0,sK1,sK2),findmin_pqp_res(sK0))
    | spl5_2 ),
    inference(resolution,[],[f142,f351]) ).

fof(f351,plain,
    ( ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
    | spl5_2 ),
    inference(avatar_component_clause,[],[f349]) ).

fof(f349,plain,
    ( spl5_2
  <=> contains_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1] :
      ( contains_pq(i(triple(X0,X1,X2)),X3)
      | ~ contains_cpq(triple(X0,X1,X2),X3) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_pq(i(triple(X0,X1,X2)),X3) )
      & ( contains_pq(i(triple(X0,X1,X2)),X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_cpq(triple(X0,X1,X2),X3)
    <=> contains_pq(i(triple(X0,X1,X2)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l8_li56) ).

fof(f195,plain,
    ! [X2,X0,X1] :
      ( contains_slb(X1,findmin_pqp_res(X0))
      | findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ( ~ contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    inference(rectify,[],[f47]) ).

fof(f47,axiom,
    ! [X0,X1,X2,X3] :
      ( ( ~ contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).

fof(f1490,plain,
    ( spl5_3
    | spl5_4 ),
    inference(avatar_split_clause,[],[f1480,f1488,f1485]) ).

fof(f1485,plain,
    ( spl5_3
  <=> ! [X4,X3] :
        ( ~ less_than(X3,X4)
        | ~ strictly_less_than(X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f1488,plain,
    ( spl5_4
  <=> ! [X2,X0,X1] : ~ check_cpq(triple(X0,X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f1480,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ check_cpq(triple(X0,X1,X2))
      | ~ less_than(X3,X4)
      | ~ strictly_less_than(X4,X3) ),
    inference(resolution,[],[f208,f206]) ).

fof(f206,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ strictly_less_than(X3,X4) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ strictly_less_than(X3,X4) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
    inference(flattening,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
    inference(true_and_false_elimination,[],[f38]) ).

fof(f38,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f208,plain,
    ! [X2,X3,X0,X1,X4] :
      ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ check_cpq(triple(X0,X1,X2))
      | ~ less_than(X4,X3) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
          | ~ check_cpq(triple(X0,X1,X2)) )
        & ( check_cpq(triple(X0,X1,X2))
          | ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ) )
      | ~ less_than(X4,X3) ),
    inference(nnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> check_cpq(triple(X0,X1,X2)) )
      | ~ less_than(X4,X3) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( less_than(X4,X3)
     => ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> check_cpq(triple(X0,X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

fof(f352,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f342,f349,f345]) ).

fof(f342,plain,
    ( ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
    | create_slb = sK1 ),
    inference(superposition,[],[f139,f189]) ).

fof(f189,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    inference(rectify,[],[f51]) ).

fof(f51,axiom,
    ! [X0,X1,X2,X3] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).

fof(f139,plain,
    ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
    inference(cnf_transformation,[],[f122]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37  % Computer : n011.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Tue Apr 30 04:41:01 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.38  % (11127)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39  % (11130)WARNING: value z3 for option sas not known
% 0.14/0.39  % (11133)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)
% 0.14/0.39  % (11132)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)
% 0.14/0.39  % (11134)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)
% 0.14/0.39  % (11130)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)
% 0.14/0.39  % (11129)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (11131)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40  % (11128)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40  TRYING [1]
% 0.14/0.40  TRYING [2]
% 0.14/0.42  TRYING [3]
% 0.14/0.43  TRYING [1]
% 0.14/0.44  TRYING [2]
% 0.21/0.47  % (11130)First to succeed.
% 0.21/0.47  % (11130)Refutation found. Thanks to Tanya!
% 0.21/0.47  % SZS status Theorem for theBenchmark
% 0.21/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.47  % (11130)------------------------------
% 0.21/0.47  % (11130)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.47  % (11130)Termination reason: Refutation
% 0.21/0.47  
% 0.21/0.47  % (11130)Memory used [KB]: 1588
% 0.21/0.47  % (11130)Time elapsed: 0.073 s
% 0.21/0.47  % (11130)Instructions burned: 152 (million)
% 0.21/0.47  % (11130)------------------------------
% 0.21/0.47  % (11130)------------------------------
% 0.21/0.47  % (11127)Success in time 0.091 s
%------------------------------------------------------------------------------