TSTP Solution File: CSR015+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : CSR015+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Sun May  5 04:56:46 EDT 2024

% Result   : Theorem 0.16s 0.41s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   67 (  16 unt;   0 def)
%            Number of atoms       :  306 ( 119 equ)
%            Maximal formula atoms :   19 (   4 avg)
%            Number of connectives :  355 ( 116   ~; 119   |; 102   &)
%                                         (  16 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :  120 ( 120   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2040,plain,
    $false,
    inference(subsumption_resolution,[],[f2039,f184]) ).

fof(f184,plain,
    holdsAt(backwards,n1),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    holdsAt(backwards,n1),
    inference(flattening,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ~ holdsAt(backwards,n1),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ~ holdsAt(backwards,n1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_backwards_1) ).

fof(f2039,plain,
    ~ holdsAt(backwards,n1),
    inference(forward_demodulation,[],[f2037,f199]) ).

fof(f199,plain,
    n1 = plus(n0,n1),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    n1 = plus(n0,n1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus0_1) ).

fof(f2037,plain,
    ~ holdsAt(backwards,plus(n0,n1)),
    inference(unit_resulting_resolution,[],[f901,f2022,f256]) ).

fof(f256,plain,
    ! [X2,X0,X1] :
      ( ~ terminates(X0,X2,X1)
      | ~ holdsAt(X2,plus(X1,n1))
      | ~ happens(X0,X1) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ~ holdsAt(X2,plus(X1,n1))
      | ~ terminates(X0,X2,X1)
      | ~ happens(X0,X1) ),
    inference(flattening,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( ~ holdsAt(X2,plus(X1,n1))
      | ~ terminates(X0,X2,X1)
      | ~ happens(X0,X1) ),
    inference(ennf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ( terminates(X0,X2,X1)
        & happens(X0,X1) )
     => ~ holdsAt(X2,plus(X1,n1)) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X3,X4,X1] :
      ( ( terminates(X3,X1,X4)
        & happens(X3,X4) )
     => ~ holdsAt(X1,plus(X4,n1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',happens_terminates_not_holds) ).

fof(f2022,plain,
    terminates(push,backwards,n0),
    inference(unit_resulting_resolution,[],[f2020,f1051]) ).

fof(f1051,plain,
    ! [X0] :
      ( terminates(push,backwards,X0)
      | happens(pull,X0) ),
    inference(resolution,[],[f301,f334]) ).

fof(f334,plain,
    ! [X0] :
      ( sP7(X0,backwards,push)
      | happens(pull,X0) ),
    inference(equality_resolution,[],[f333]) ).

fof(f333,plain,
    ! [X2,X0] :
      ( sP7(X0,backwards,X2)
      | happens(pull,X0)
      | push != X2 ),
    inference(equality_resolution,[],[f299]) ).

fof(f299,plain,
    ! [X2,X0,X1] :
      ( sP7(X0,X1,X2)
      | happens(pull,X0)
      | backwards != X1
      | push != X2 ),
    inference(cnf_transformation,[],[f181]) ).

fof(f181,plain,
    ! [X0,X1,X2] :
      ( ( sP7(X0,X1,X2)
        | happens(pull,X0)
        | backwards != X1
        | push != X2 )
      & ( ( ~ happens(pull,X0)
          & backwards = X1
          & push = X2 )
        | ~ sP7(X0,X1,X2) ) ),
    inference(rectify,[],[f180]) ).

fof(f180,plain,
    ! [X2,X1,X0] :
      ( ( sP7(X2,X1,X0)
        | happens(pull,X2)
        | backwards != X1
        | push != X0 )
      & ( ( ~ happens(pull,X2)
          & backwards = X1
          & push = X0 )
        | ~ sP7(X2,X1,X0) ) ),
    inference(flattening,[],[f179]) ).

fof(f179,plain,
    ! [X2,X1,X0] :
      ( ( sP7(X2,X1,X0)
        | happens(pull,X2)
        | backwards != X1
        | push != X0 )
      & ( ( ~ happens(pull,X2)
          & backwards = X1
          & push = X0 )
        | ~ sP7(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X2,X1,X0] :
      ( sP7(X2,X1,X0)
    <=> ( ~ happens(pull,X2)
        & backwards = X1
        & push = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f301,plain,
    ! [X2,X0,X1] :
      ( ~ sP7(X2,X1,X0)
      | terminates(X0,X1,X2) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,plain,
    ! [X0,X1,X2] :
      ( ( terminates(X0,X1,X2)
        | ( ~ sP12(X2,X1,X0)
          & ~ sP11(X2,X1,X0)
          & ~ sP10(X2,X1,X0)
          & ~ sP9(X2,X1,X0)
          & ~ sP8(X2,X1,X0)
          & ~ sP7(X2,X1,X0) ) )
      & ( sP12(X2,X1,X0)
        | sP11(X2,X1,X0)
        | sP10(X2,X1,X0)
        | sP9(X2,X1,X0)
        | sP8(X2,X1,X0)
        | sP7(X2,X1,X0)
        | ~ terminates(X0,X1,X2) ) ),
    inference(flattening,[],[f182]) ).

fof(f182,plain,
    ! [X0,X1,X2] :
      ( ( terminates(X0,X1,X2)
        | ( ~ sP12(X2,X1,X0)
          & ~ sP11(X2,X1,X0)
          & ~ sP10(X2,X1,X0)
          & ~ sP9(X2,X1,X0)
          & ~ sP8(X2,X1,X0)
          & ~ sP7(X2,X1,X0) ) )
      & ( sP12(X2,X1,X0)
        | sP11(X2,X1,X0)
        | sP10(X2,X1,X0)
        | sP9(X2,X1,X0)
        | sP8(X2,X1,X0)
        | sP7(X2,X1,X0)
        | ~ terminates(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0,X1,X2] :
      ( terminates(X0,X1,X2)
    <=> ( sP12(X2,X1,X0)
        | sP11(X2,X1,X0)
        | sP10(X2,X1,X0)
        | sP9(X2,X1,X0)
        | sP8(X2,X1,X0)
        | sP7(X2,X1,X0) ) ),
    inference(definition_folding,[],[f77,f117,f116,f115,f114,f113,f112]) ).

fof(f113,plain,
    ! [X2,X1,X0] :
      ( sP8(X2,X1,X0)
    <=> ( ~ happens(push,X2)
        & forwards = X1
        & pull = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f114,plain,
    ! [X2,X1,X0] :
      ( sP9(X2,X1,X0)
    <=> ( happens(push,X2)
        & forwards = X1
        & pull = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

fof(f115,plain,
    ! [X2,X1,X0] :
      ( sP10(X2,X1,X0)
    <=> ( happens(push,X2)
        & backwards = X1
        & pull = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

fof(f116,plain,
    ! [X2,X1,X0] :
      ( sP11(X2,X1,X0)
    <=> ( ~ happens(pull,X2)
        & spinning = X1
        & push = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

fof(f117,plain,
    ! [X2,X1,X0] :
      ( sP12(X2,X1,X0)
    <=> ( ~ happens(push,X2)
        & spinning = X1
        & pull = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( terminates(X0,X1,X2)
    <=> ( ( ~ happens(push,X2)
          & spinning = X1
          & pull = X0 )
        | ( ~ happens(pull,X2)
          & spinning = X1
          & push = X0 )
        | ( happens(push,X2)
          & backwards = X1
          & pull = X0 )
        | ( happens(push,X2)
          & forwards = X1
          & pull = X0 )
        | ( ~ happens(push,X2)
          & forwards = X1
          & pull = X0 )
        | ( ~ happens(pull,X2)
          & backwards = X1
          & push = X0 ) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3,X1,X4] :
      ( terminates(X3,X1,X4)
    <=> ( ( ~ happens(push,X4)
          & spinning = X1
          & pull = X3 )
        | ( ~ happens(pull,X4)
          & spinning = X1
          & push = X3 )
        | ( happens(push,X4)
          & backwards = X1
          & pull = X3 )
        | ( happens(push,X4)
          & forwards = X1
          & pull = X3 )
        | ( ~ happens(push,X4)
          & forwards = X1
          & pull = X3 )
        | ( ~ happens(pull,X4)
          & backwards = X1
          & push = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',terminates_all_defn) ).

fof(f2020,plain,
    ~ happens(pull,n0),
    inference(subsumption_resolution,[],[f2019,f184]) ).

fof(f2019,plain,
    ( ~ holdsAt(backwards,n1)
    | ~ happens(pull,n0) ),
    inference(forward_demodulation,[],[f2007,f199]) ).

fof(f2007,plain,
    ( ~ holdsAt(backwards,plus(n0,n1))
    | ~ happens(pull,n0) ),
    inference(resolution,[],[f256,f1058]) ).

fof(f1058,plain,
    terminates(pull,backwards,n0),
    inference(unit_resulting_resolution,[],[f1000,f304]) ).

fof(f304,plain,
    ! [X2,X0,X1] :
      ( ~ sP10(X2,X1,X0)
      | terminates(X0,X1,X2) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f1000,plain,
    sP10(n0,backwards,pull),
    inference(unit_resulting_resolution,[],[f901,f328]) ).

fof(f328,plain,
    ! [X0] :
      ( ~ happens(push,X0)
      | sP10(X0,backwards,pull) ),
    inference(equality_resolution,[],[f327]) ).

fof(f327,plain,
    ! [X2,X0] :
      ( sP10(X0,backwards,X2)
      | ~ happens(push,X0)
      | pull != X2 ),
    inference(equality_resolution,[],[f287]) ).

fof(f287,plain,
    ! [X2,X0,X1] :
      ( sP10(X0,X1,X2)
      | ~ happens(push,X0)
      | backwards != X1
      | pull != X2 ),
    inference(cnf_transformation,[],[f172]) ).

fof(f172,plain,
    ! [X0,X1,X2] :
      ( ( sP10(X0,X1,X2)
        | ~ happens(push,X0)
        | backwards != X1
        | pull != X2 )
      & ( ( happens(push,X0)
          & backwards = X1
          & pull = X2 )
        | ~ sP10(X0,X1,X2) ) ),
    inference(rectify,[],[f171]) ).

fof(f171,plain,
    ! [X2,X1,X0] :
      ( ( sP10(X2,X1,X0)
        | ~ happens(push,X2)
        | backwards != X1
        | pull != X0 )
      & ( ( happens(push,X2)
          & backwards = X1
          & pull = X0 )
        | ~ sP10(X2,X1,X0) ) ),
    inference(flattening,[],[f170]) ).

fof(f170,plain,
    ! [X2,X1,X0] :
      ( ( sP10(X2,X1,X0)
        | ~ happens(push,X2)
        | backwards != X1
        | pull != X0 )
      & ( ( happens(push,X2)
          & backwards = X1
          & pull = X0 )
        | ~ sP10(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f115]) ).

fof(f901,plain,
    happens(push,n0),
    inference(unit_resulting_resolution,[],[f631,f253]) ).

fof(f253,plain,
    ! [X0,X1] :
      ( ~ sP3(X1,X0)
      | happens(X0,X1) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ( happens(X0,X1)
        | ~ sP3(X1,X0) )
      & ( sP3(X1,X0)
        | ~ happens(X0,X1) ) ),
    inference(nnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( happens(X0,X1)
    <=> sP3(X1,X0) ),
    inference(definition_folding,[],[f69,f106,f105,f104,f103]) ).

fof(f103,plain,
    ! [X1,X0] :
      ( sP0(X1,X0)
    <=> ( n0 = X1
        & push = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f104,plain,
    ! [X1,X0] :
      ( sP1(X1,X0)
    <=> ( n1 = X1
        & pull = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f105,plain,
    ! [X1,X0] :
      ( sP2(X1,X0)
    <=> ( n2 = X1
        & pull = X0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f106,plain,
    ! [X1,X0] :
      ( sP3(X1,X0)
    <=> ( ( n2 = X1
          & push = X0 )
        | sP2(X1,X0)
        | sP1(X1,X0)
        | sP0(X1,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( happens(X0,X1)
    <=> ( ( n2 = X1
          & push = X0 )
        | ( n2 = X1
          & pull = X0 )
        | ( n1 = X1
          & pull = X0 )
        | ( n0 = X1
          & push = X0 ) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X3,X4] :
      ( happens(X3,X4)
    <=> ( ( n2 = X4
          & push = X3 )
        | ( n2 = X4
          & pull = X3 )
        | ( n1 = X4
          & pull = X3 )
        | ( n0 = X4
          & push = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',happens_all_defn) ).

fof(f631,plain,
    sP3(n0,push),
    inference(unit_resulting_resolution,[],[f316,f239]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | sP3(X0,X1) ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ( sP3(X0,X1)
        | ( ( n2 != X0
            | push != X1 )
          & ~ sP2(X0,X1)
          & ~ sP1(X0,X1)
          & ~ sP0(X0,X1) ) )
      & ( ( n2 = X0
          & push = X1 )
        | sP2(X0,X1)
        | sP1(X0,X1)
        | sP0(X0,X1)
        | ~ sP3(X0,X1) ) ),
    inference(rectify,[],[f141]) ).

fof(f141,plain,
    ! [X1,X0] :
      ( ( sP3(X1,X0)
        | ( ( n2 != X1
            | push != X0 )
          & ~ sP2(X1,X0)
          & ~ sP1(X1,X0)
          & ~ sP0(X1,X0) ) )
      & ( ( n2 = X1
          & push = X0 )
        | sP2(X1,X0)
        | sP1(X1,X0)
        | sP0(X1,X0)
        | ~ sP3(X1,X0) ) ),
    inference(flattening,[],[f140]) ).

fof(f140,plain,
    ! [X1,X0] :
      ( ( sP3(X1,X0)
        | ( ( n2 != X1
            | push != X0 )
          & ~ sP2(X1,X0)
          & ~ sP1(X1,X0)
          & ~ sP0(X1,X0) ) )
      & ( ( n2 = X1
          & push = X0 )
        | sP2(X1,X0)
        | sP1(X1,X0)
        | sP0(X1,X0)
        | ~ sP3(X1,X0) ) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f316,plain,
    sP0(n0,push),
    inference(equality_resolution,[],[f315]) ).

fof(f315,plain,
    ! [X1] :
      ( sP0(n0,X1)
      | push != X1 ),
    inference(equality_resolution,[],[f251]) ).

fof(f251,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | n0 != X0
      | push != X1 ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | n0 != X0
        | push != X1 )
      & ( ( n0 = X0
          & push = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f150]) ).

fof(f150,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | n0 != X1
        | push != X0 )
      & ( ( n0 = X1
          & push = X0 )
        | ~ sP0(X1,X0) ) ),
    inference(flattening,[],[f149]) ).

fof(f149,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | n0 != X1
        | push != X0 )
      & ( ( n0 = X1
          & push = X0 )
        | ~ sP0(X1,X0) ) ),
    inference(nnf_transformation,[],[f103]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : CSR015+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.11/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n023.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 20:06:38 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  % (1607)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38  % (1610)WARNING: value z3 for option sas not known
% 0.16/0.38  % (1611)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38  % (1614)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)
% 0.16/0.38  % (1612)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)
% 0.16/0.38  % (1613)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)
% 0.16/0.38  % (1608)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38  % (1609)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38  % (1610)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)
% 0.16/0.39  Detected minimum model sizes of [3]
% 0.16/0.39  Detected maximum model sizes of [max]
% 0.16/0.39  TRYING [3]
% 0.16/0.41  TRYING [4]
% 0.16/0.41  % (1614)First to succeed.
% 0.16/0.41  % (1614)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1607"
% 0.16/0.41  % (1614)Refutation found. Thanks to Tanya!
% 0.16/0.41  % SZS status Theorem for theBenchmark
% 0.16/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.41  % (1614)------------------------------
% 0.16/0.41  % (1614)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.41  % (1614)Termination reason: Refutation
% 0.16/0.41  
% 0.16/0.41  % (1614)Memory used [KB]: 1199
% 0.16/0.41  % (1614)Time elapsed: 0.031 s
% 0.16/0.41  % (1614)Instructions burned: 56 (million)
% 0.16/0.41  % (1607)Success in time 0.038 s
%------------------------------------------------------------------------------