TSTP Solution File: NUM316+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM316+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n022.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 08:18:44 EDT 2024

% Result   : Theorem 11.31s 1.99s
% Output   : Refutation 11.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   47 (  27 unt;   0 def)
%            Number of atoms       :  106 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  109 (  50   ~;  41   |;  11   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-1 aty)
%            Number of variables   :   92 (  92   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f170058,plain,
    $false,
    inference(subsumption_resolution,[],[f170057,f95570]) ).

fof(f95570,plain,
    rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
    inference(unit_resulting_resolution,[],[f769,f755,f871]) ).

fof(f871,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(cnf_transformation,[],[f456]) ).

fof(f456,plain,
    ! [X0,X1,X2,X3,X4] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(flattening,[],[f455]) ).

fof(f455,plain,
    ! [X0,X1,X2,X3,X4] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
      | ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
    inference(ennf_transformation,[],[f417]) ).

fof(f417,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
        & rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) )
     => rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
    inference(rectify,[],[f297]) ).

fof(f297,axiom,
    ! [X20,X21,X22,X23,X24] :
      ( ( rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(n0))
        & rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(n0)) )
     => rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdnn(X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).

fof(f755,plain,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f352]) ).

fof(f352,axiom,
    rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n0_n5_n0) ).

fof(f769,plain,
    rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
    inference(cnf_transformation,[],[f325]) ).

fof(f325,axiom,
    rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n2_n3_n5_n0) ).

fof(f170057,plain,
    ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
    inference(unit_resulting_resolution,[],[f131438,f510,f129828,f899]) ).

fof(f899,plain,
    ! [X3,X0,X4,X5] :
      ( ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
      | ~ rdn_positive_less(X3,X4)
      | ~ rdn_translate(X0,rdn_pos(X3))
      | sP9(X4,X0,X5) ),
    inference(cnf_transformation,[],[f899_D]) ).

fof(f899_D,plain,
    ! [X5,X0,X4] :
      ( ! [X3] :
          ( ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
          | ~ rdn_positive_less(X3,X4)
          | ~ rdn_translate(X0,rdn_pos(X3)) )
    <=> ~ sP9(X4,X0,X5) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).

fof(f129828,plain,
    ~ sP9(rdnn(n5),n2,rdnn(n3)),
    inference(unit_resulting_resolution,[],[f501,f89924,f900]) ).

fof(f900,plain,
    ! [X0,X1,X4,X5] :
      ( ~ sP9(X4,X0,X5)
      | ~ sP8(X0,X5,X1)
      | ~ rdn_translate(X1,rdn_neg(X4)) ),
    inference(general_splitting,[],[f898,f899_D]) ).

fof(f898,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
      | ~ rdn_positive_less(X3,X4)
      | ~ rdn_translate(X1,rdn_neg(X4))
      | ~ rdn_translate(X0,rdn_pos(X3))
      | ~ sP8(X0,X5,X1) ),
    inference(general_splitting,[],[f874,f897_D]) ).

fof(f897,plain,
    ! [X2,X0,X1,X5] :
      ( ~ rdn_translate(X2,rdn_neg(X5))
      | sum(X0,X1,X2)
      | sP8(X0,X5,X1) ),
    inference(cnf_transformation,[],[f897_D]) ).

fof(f897_D,plain,
    ! [X1,X5,X0] :
      ( ! [X2] :
          ( ~ rdn_translate(X2,rdn_neg(X5))
          | sum(X0,X1,X2) )
    <=> ~ sP8(X0,X5,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP8])]) ).

fof(f874,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_neg(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
      | ~ rdn_positive_less(X3,X4)
      | ~ rdn_translate(X1,rdn_neg(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(cnf_transformation,[],[f461]) ).

fof(f461,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_neg(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
      | ~ rdn_positive_less(X3,X4)
      | ~ rdn_translate(X1,rdn_neg(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(flattening,[],[f460]) ).

fof(f460,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_neg(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
      | ~ rdn_positive_less(X3,X4)
      | ~ rdn_translate(X1,rdn_neg(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(ennf_transformation,[],[f420]) ).

fof(f420,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( rdn_translate(X2,rdn_neg(X5))
        & rdn_add_with_carry(rdnn(n0),X3,X5,X4)
        & rdn_positive_less(X3,X4)
        & rdn_translate(X1,rdn_neg(X4))
        & rdn_translate(X0,rdn_pos(X3)) )
     => sum(X0,X1,X2) ),
    inference(rectify,[],[f289]) ).

fof(f289,axiom,
    ! [X0,X1,X2,X9,X10,X11] :
      ( ( rdn_translate(X2,rdn_neg(X11))
        & rdn_add_with_carry(rdnn(n0),X9,X11,X10)
        & rdn_positive_less(X9,X10)
        & rdn_translate(X1,rdn_neg(X10))
        & rdn_translate(X0,rdn_pos(X9)) )
     => sum(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_neg_1) ).

fof(f89924,plain,
    sP8(n2,rdnn(n3),nn5),
    inference(unit_resulting_resolution,[],[f475,f502,f897]) ).

fof(f502,plain,
    rdn_translate(nn3,rdn_neg(rdnn(n3))),
    inference(cnf_transformation,[],[f131]) ).

fof(f131,axiom,
    rdn_translate(nn3,rdn_neg(rdnn(n3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn3) ).

fof(f475,plain,
    ~ sum(n2,nn5,nn3),
    inference(cnf_transformation,[],[f404]) ).

fof(f404,plain,
    ~ sum(n2,nn5,nn3),
    inference(flattening,[],[f403]) ).

fof(f403,negated_conjecture,
    ~ sum(n2,nn5,nn3),
    inference(negated_conjecture,[],[f402]) ).

fof(f402,conjecture,
    sum(n2,nn5,nn3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_nn5_nn3) ).

fof(f501,plain,
    rdn_translate(nn5,rdn_neg(rdnn(n5))),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,axiom,
    rdn_translate(nn5,rdn_neg(rdnn(n5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn5) ).

fof(f510,plain,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    rdn_translate(n2,rdn_pos(rdnn(n2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn2) ).

fof(f131438,plain,
    rdn_positive_less(rdnn(n2),rdnn(n5)),
    inference(unit_resulting_resolution,[],[f490,f91848,f860]) ).

fof(f860,plain,
    ! [X2,X0,X1] :
      ( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
      | rdn_positive_less(rdnn(X0),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
    inference(cnf_transformation,[],[f439]) ).

fof(f439,plain,
    ! [X0,X1,X2] :
      ( rdn_positive_less(rdnn(X0),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X1),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
    inference(flattening,[],[f438]) ).

fof(f438,plain,
    ! [X0,X1,X2] :
      ( rdn_positive_less(rdnn(X0),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X1),rdnn(X2))
      | ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
    inference(ennf_transformation,[],[f275]) ).

fof(f275,axiom,
    ! [X0,X1,X2] :
      ( ( rdn_positive_less(rdnn(X1),rdnn(X2))
        & rdn_positive_less(rdnn(X0),rdnn(X1)) )
     => rdn_positive_less(rdnn(X0),rdnn(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).

fof(f91848,plain,
    rdn_positive_less(rdnn(n2),rdnn(n4)),
    inference(unit_resulting_resolution,[],[f491,f487,f860]) ).

fof(f487,plain,
    rdn_positive_less(rdnn(n3),rdnn(n4)),
    inference(cnf_transformation,[],[f269]) ).

fof(f269,axiom,
    rdn_positive_less(rdnn(n3),rdnn(n4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less34) ).

fof(f491,plain,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    inference(cnf_transformation,[],[f268]) ).

fof(f268,axiom,
    rdn_positive_less(rdnn(n2),rdnn(n3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less23) ).

fof(f490,plain,
    rdn_positive_less(rdnn(n4),rdnn(n5)),
    inference(cnf_transformation,[],[f270]) ).

fof(f270,axiom,
    rdn_positive_less(rdnn(n4),rdnn(n5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less45) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM316+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 15:03:07 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (3259)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38  % (3263)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38  % (3264)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)
% 0.20/0.38  % (3266)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)
% 0.20/0.38  % (3265)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)
% 0.20/0.39  % (3261)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.39  % (3262)WARNING: value z3 for option sas not known
% 0.20/0.39  % (3260)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.39  % (3262)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)
% 0.20/0.42  TRYING [1]
% 0.20/0.42  TRYING [2]
% 0.20/0.46  TRYING [1]
% 0.20/0.47  TRYING [3]
% 0.20/0.48  TRYING [2]
% 0.20/0.54  TRYING [3]
% 2.11/0.68  TRYING [4]
% 2.11/0.72  TRYING [4]
% 7.01/1.39  TRYING [5]
% 7.84/1.52  TRYING [1]
% 7.84/1.52  TRYING [2]
% 8.31/1.57  TRYING [3]
% 9.21/1.68  TRYING [5]
% 9.80/1.77  TRYING [4]
% 11.31/1.99  % (3266)First to succeed.
% 11.31/1.99  % (3266)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3259"
% 11.31/1.99  % (3266)Refutation found. Thanks to Tanya!
% 11.31/1.99  % SZS status Theorem for theBenchmark
% 11.31/1.99  % SZS output start Proof for theBenchmark
% See solution above
% 11.31/1.99  % (3266)------------------------------
% 11.31/1.99  % (3266)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 11.31/1.99  % (3266)Termination reason: Refutation
% 11.31/1.99  
% 11.31/1.99  % (3266)Memory used [KB]: 39911
% 11.31/1.99  % (3266)Time elapsed: 1.604 s
% 11.31/1.99  % (3266)Instructions burned: 5005 (million)
% 11.31/1.99  % (3259)Success in time 1.632 s
%------------------------------------------------------------------------------