TSTP Solution File: NUM848+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM848+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 08:42:34 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   60 (  30 unt;   0 def)
%            Number of atoms       :  110 (  45 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   90 (  40   ~;  30   |;  10   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   7 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   65 (  65   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f281,plain,
    $false,
    inference(avatar_sat_refutation,[],[f253,f257,f261,f265,f269,f274,f280]) ).

fof(f280,plain,
    spl4_6,
    inference(avatar_contradiction_clause,[],[f279]) ).

fof(f279,plain,
    ( $false
    | spl4_6 ),
    inference(trivial_inequality_removal,[],[f278]) ).

fof(f278,plain,
    ( vplus(vmul(vd437,vd436),vmul(vd436,vplus(vd439,v1))) != vplus(vmul(vd437,vd436),vmul(vd436,vplus(vd439,v1)))
    | spl4_6 ),
    inference(forward_demodulation,[],[f277,f169]) ).

fof(f169,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(rectify,[],[f49]) ).

fof(f49,axiom,
    ! [X70,X71] : vplus(X71,X70) = vplus(X70,X71),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof(f277,plain,
    ( vplus(vmul(vd437,vd436),vmul(vd436,vplus(vd439,v1))) != vplus(vmul(vd437,vd436),vmul(vd436,vplus(v1,vd439)))
    | spl4_6 ),
    inference(forward_demodulation,[],[f276,f230]) ).

fof(f230,plain,
    ! [X0,X1] : vplus(vmul(X0,X1),X0) = vmul(X0,vplus(v1,X1)),
    inference(definition_unfolding,[],[f174,f164]) ).

fof(f164,plain,
    ! [X0] : vsucc(X0) = vplus(v1,X0),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] : vsucc(X0) = vplus(v1,X0),
    inference(rectify,[],[f51]) ).

fof(f51,axiom,
    ! [X74] : vplus(v1,X74) = vsucc(X74),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).

fof(f174,plain,
    ! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( vmul(X0,v1) = X0
      & vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X5,X6] :
      ( vmul(X5,v1) = X5
      & vmul(X5,vsucc(X6)) = vplus(vmul(X5,X6),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).

fof(f276,plain,
    ( vplus(vmul(vd437,vd436),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd437,vd436),vmul(vd436,vplus(vd439,v1)))
    | spl4_6 ),
    inference(forward_demodulation,[],[f275,f168]) ).

fof(f168,plain,
    ! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

fof(f275,plain,
    ( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vplus(vd439,v1)))
    | spl4_6 ),
    inference(forward_demodulation,[],[f273,f169]) ).

fof(f273,plain,
    ( vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439)))
    | spl4_6 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f271,plain,
    ( spl4_6
  <=> vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f274,plain,
    ~ spl4_6,
    inference(avatar_split_clause,[],[f218,f271]) ).

fof(f218,plain,
    vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439))),
    inference(definition_unfolding,[],[f151,f164]) ).

fof(f151,plain,
    vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
    inference(flattening,[],[f2]) ).

fof(f2,negated_conjecture,
    vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 4)') ).

fof(f269,plain,
    spl4_5,
    inference(avatar_split_clause,[],[f239,f267]) ).

fof(f267,plain,
    ( spl4_5
  <=> ! [X1] : geq(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f239,plain,
    ! [X1] : geq(X1,X1),
    inference(equality_resolution,[],[f198]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( geq(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ( geq(X1,X0)
        | ( X0 != X1
          & ~ greater(X1,X0) ) )
      & ( X0 = X1
        | greater(X1,X0)
        | ~ geq(X1,X0) ) ),
    inference(flattening,[],[f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( ( geq(X1,X0)
        | ( X0 != X1
          & ~ greater(X1,X0) ) )
      & ( X0 = X1
        | greater(X1,X0)
        | ~ geq(X1,X0) ) ),
    inference(nnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( geq(X1,X0)
    <=> ( X0 = X1
        | greater(X1,X0) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ! [X47,X48] :
      ( geq(X48,X47)
    <=> ( X47 = X48
        | greater(X48,X47) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).

fof(f265,plain,
    spl4_4,
    inference(avatar_split_clause,[],[f238,f263]) ).

fof(f263,plain,
    ( spl4_4
  <=> ! [X1] : leq(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f238,plain,
    ! [X1] : leq(X1,X1),
    inference(equality_resolution,[],[f195]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ( leq(X1,X0)
        | ( X0 != X1
          & ~ less(X1,X0) ) )
      & ( X0 = X1
        | less(X1,X0)
        | ~ leq(X1,X0) ) ),
    inference(flattening,[],[f139]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ( leq(X1,X0)
        | ( X0 != X1
          & ~ less(X1,X0) ) )
      & ( X0 = X1
        | less(X1,X0)
        | ~ leq(X1,X0) ) ),
    inference(nnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
    <=> ( X0 = X1
        | less(X1,X0) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,axiom,
    ! [X45,X46] :
      ( leq(X46,X45)
    <=> ( X45 = X46
        | less(X46,X45) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).

fof(f261,plain,
    spl4_3,
    inference(avatar_split_clause,[],[f234,f259]) ).

fof(f259,plain,
    ( spl4_3
  <=> ! [X1] : ~ greater(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f234,plain,
    ! [X1] : ~ greater(X1,X1),
    inference(equality_resolution,[],[f177]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | X0 != X1 ),
    inference(rectify,[],[f40]) ).

fof(f40,axiom,
    ! [X53,X54] :
      ( ~ greater(X53,X54)
      | X53 != X54 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).

fof(f257,plain,
    spl4_2,
    inference(avatar_split_clause,[],[f233,f255]) ).

fof(f255,plain,
    ( spl4_2
  <=> ! [X1] : ~ less(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f233,plain,
    ! [X1] : ~ less(X1,X1),
    inference(equality_resolution,[],[f176]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | X0 != X1 ),
    inference(rectify,[],[f38]) ).

fof(f38,axiom,
    ! [X53,X54] :
      ( ~ less(X53,X54)
      | X53 != X54 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).

fof(f253,plain,
    spl4_1,
    inference(avatar_split_clause,[],[f160,f251]) ).

fof(f251,plain,
    ( spl4_1
  <=> ! [X0] : geq(X0,v1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f160,plain,
    ! [X0] : geq(X0,v1),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0] : geq(X0,v1),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X11] : geq(X11,v1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM848+1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n005.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   : Fri May  3 15:12:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (22487)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (22490)WARNING: value z3 for option sas not known
% 0.13/0.37  % (22491)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (22489)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (22488)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (22493)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)
% 0.13/0.37  % (22492)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)
% 0.13/0.37  % (22494)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)
% 0.13/0.37  % (22490)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)
% 0.13/0.37  % (22492)First to succeed.
% 0.13/0.37  TRYING [1]
% 0.13/0.37  % (22492)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22487"
% 0.13/0.37  TRYING [2]
% 0.13/0.37  % (22492)Refutation found. Thanks to Tanya!
% 0.13/0.37  % SZS status Theorem for theBenchmark
% 0.13/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37  % (22492)------------------------------
% 0.13/0.37  % (22492)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (22492)Termination reason: Refutation
% 0.13/0.37  
% 0.13/0.37  % (22492)Memory used [KB]: 885
% 0.13/0.37  % (22492)Time elapsed: 0.006 s
% 0.13/0.37  % (22492)Instructions burned: 8 (million)
% 0.13/0.37  % (22487)Success in time 0.012 s
%------------------------------------------------------------------------------