TSTP Solution File: NUM331+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM331+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n027.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 May 21 01:49:34 EDT 2024

% Result   : Theorem 108.39s 15.87s
% Output   : Refutation 108.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   61 (  30 unt;   0 def)
%            Number of atoms       :  142 (  15 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  143 (  62   ~;  43   |;  25   &)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :  138 ( 132   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1001674,plain,
    $false,
    inference(subsumption_resolution,[],[f1001673,f135594]) ).

fof(f135594,plain,
    rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))),
    inference(unit_resulting_resolution,[],[f761,f93830,f916]) ).

fof(f916,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ sP16(X5,X3,X4,X0)
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5))
      | rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1))) ),
    inference(general_splitting,[],[f883,f915_D]) ).

fof(f915,plain,
    ! [X3,X0,X6,X4,X5] :
      ( ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
      | sP16(X5,X3,X4,X0) ),
    inference(cnf_transformation,[],[f915_D]) ).

fof(f915_D,plain,
    ! [X0,X4,X3,X5] :
      ( ! [X6] :
          ( ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
          | ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6)) )
    <=> ~ sP16(X5,X3,X4,X0) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP16])]) ).

fof(f883,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1)))
      | ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5)) ),
    inference(cnf_transformation,[],[f469]) ).

fof(f469,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1)))
      | ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5)) ),
    inference(flattening,[],[f468]) ).

fof(f468,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1)))
      | ~ rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
      | ~ rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
      | ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5)) ),
    inference(ennf_transformation,[],[f423]) ).

fof(f423,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( rdn_digit_add(rdnn(X5),rdnn(X6),rdnn(n1),rdnn(n0))
        & rdn_digit_add(rdnn(X3),rdnn(X0),rdnn(X4),rdnn(X6))
        & rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(X5)) )
     => rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdn(rdnn(X4),rdnn(n1))) ),
    inference(rectify,[],[f298]) ).

fof(f298,axiom,
    ! [X20,X21,X22,X24,X23,X25,X26] :
      ( ( rdn_digit_add(rdnn(X25),rdnn(X26),rdnn(n1),rdnn(n0))
        & rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(X26))
        & rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(X25)) )
     => rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdn(rdnn(X23),rdnn(n1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_rdn) ).

fof(f93830,plain,
    sP16(n1,n3,n3,n0),
    inference(unit_resulting_resolution,[],[f743,f797,f915]) ).

fof(f797,plain,
    rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
    inference(cnf_transformation,[],[f312]) ).

fof(f312,axiom,
    rdn_digit_add(rdnn(n1),rdnn(n0),rdnn(n1),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n1_n0_n1_n0) ).

fof(f743,plain,
    rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
    inference(cnf_transformation,[],[f332]) ).

fof(f332,axiom,
    rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n3_n0_n3_n0) ).

fof(f761,plain,
    rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
    inference(cnf_transformation,[],[f378]) ).

fof(f378,axiom,
    rdn_digit_add(rdnn(n7),rdnn(n6),rdnn(n3),rdnn(n1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n7_n6_n3_n1) ).

fof(f1001673,plain,
    ~ rdn_add_with_carry(rdnn(n0),rdnn(n7),rdnn(n6),rdn(rdnn(n3),rdnn(n1))),
    inference(unit_resulting_resolution,[],[f515,f1001672,f909]) ).

fof(f909,plain,
    ! [X3,X0,X4,X5] :
      ( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
      | ~ rdn_translate(X0,rdn_pos(X3))
      | sP13(X4,X0,X5) ),
    inference(cnf_transformation,[],[f909_D]) ).

fof(f909_D,plain,
    ! [X5,X0,X4] :
      ( ! [X3] :
          ( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
          | ~ rdn_translate(X0,rdn_pos(X3)) )
    <=> ~ sP13(X4,X0,X5) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP13])]) ).

fof(f1001672,plain,
    ~ sP13(rdnn(n6),n7,rdn(rdnn(n3),rdnn(n1))),
    inference(unit_resulting_resolution,[],[f514,f1001661,f910]) ).

fof(f910,plain,
    ! [X0,X1,X4,X5] :
      ( ~ sP13(X4,X0,X5)
      | ~ sP12(X0,X5,X1)
      | ~ rdn_translate(X1,rdn_pos(X4)) ),
    inference(general_splitting,[],[f908,f909_D]) ).

fof(f908,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
      | ~ rdn_translate(X1,rdn_pos(X4))
      | ~ rdn_translate(X0,rdn_pos(X3))
      | ~ sP12(X0,X5,X1) ),
    inference(general_splitting,[],[f881,f907_D]) ).

fof(f907,plain,
    ! [X2,X0,X1,X5] :
      ( ~ rdn_translate(X2,rdn_pos(X5))
      | sum(X0,X1,X2)
      | sP12(X0,X5,X1) ),
    inference(cnf_transformation,[],[f907_D]) ).

fof(f907_D,plain,
    ! [X1,X5,X0] :
      ( ! [X2] :
          ( ~ rdn_translate(X2,rdn_pos(X5))
          | sum(X0,X1,X2) )
    <=> ~ sP12(X0,X5,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP12])]) ).

fof(f881,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
      | ~ rdn_translate(X1,rdn_pos(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(cnf_transformation,[],[f465]) ).

fof(f465,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
      | ~ rdn_translate(X1,rdn_pos(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(flattening,[],[f464]) ).

fof(f464,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ rdn_translate(X2,rdn_pos(X5))
      | ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
      | ~ rdn_translate(X1,rdn_pos(X4))
      | ~ rdn_translate(X0,rdn_pos(X3)) ),
    inference(ennf_transformation,[],[f421]) ).

fof(f421,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( rdn_translate(X2,rdn_pos(X5))
        & rdn_add_with_carry(rdnn(n0),X3,X4,X5)
        & rdn_translate(X1,rdn_pos(X4))
        & rdn_translate(X0,rdn_pos(X3)) )
     => sum(X0,X1,X2) ),
    inference(rectify,[],[f287]) ).

fof(f287,axiom,
    ! [X0,X1,X2,X9,X10,X11] :
      ( ( rdn_translate(X2,rdn_pos(X11))
        & rdn_add_with_carry(rdnn(n0),X9,X10,X11)
        & rdn_translate(X1,rdn_pos(X10))
        & rdn_translate(X0,rdn_pos(X9)) )
     => sum(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_pos) ).

fof(f1001661,plain,
    sP12(n7,rdn(rdnn(n3),rdnn(n1)),n6),
    inference(unit_resulting_resolution,[],[f607,f1001657,f907]) ).

fof(f1001657,plain,
    ~ sum(n7,n6,n13),
    inference(superposition,[],[f88637,f1001648]) ).

fof(f1001648,plain,
    n13 = sK0,
    inference(unit_resulting_resolution,[],[f479,f1001639,f875]) ).

fof(f875,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sum(X0,X1,X3)
      | X2 = X3
      | ~ sum(X0,X1,X2) ),
    inference(cnf_transformation,[],[f454]) ).

fof(f454,plain,
    ! [X0,X1,X2,X3] :
      ( X2 = X3
      | ~ sum(X0,X1,X3)
      | ~ sum(X0,X1,X2) ),
    inference(flattening,[],[f453]) ).

fof(f453,plain,
    ! [X0,X1,X2,X3] :
      ( X2 = X3
      | ~ sum(X0,X1,X3)
      | ~ sum(X0,X1,X2) ),
    inference(ennf_transformation,[],[f415]) ).

fof(f415,plain,
    ! [X0,X1,X2,X3] :
      ( ( sum(X0,X1,X3)
        & sum(X0,X1,X2) )
     => X2 = X3 ),
    inference(rectify,[],[f293]) ).

fof(f293,axiom,
    ! [X0,X1,X14,X15] :
      ( ( sum(X0,X1,X15)
        & sum(X0,X1,X14) )
     => X14 = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_sum) ).

fof(f1001639,plain,
    sum(n6,n7,n13),
    inference(unit_resulting_resolution,[],[f607,f1001635,f907]) ).

fof(f1001635,plain,
    ~ sP12(n6,rdn(rdnn(n3),rdnn(n1)),n7),
    inference(unit_resulting_resolution,[],[f515,f1001508,f910]) ).

fof(f1001508,plain,
    sP13(rdnn(n7),n6,rdn(rdnn(n3),rdnn(n1))),
    inference(unit_resulting_resolution,[],[f514,f135593,f909]) ).

fof(f135593,plain,
    rdn_add_with_carry(rdnn(n0),rdnn(n6),rdnn(n7),rdn(rdnn(n3),rdnn(n1))),
    inference(unit_resulting_resolution,[],[f759,f93830,f916]) ).

fof(f759,plain,
    rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
    inference(cnf_transformation,[],[f369]) ).

fof(f369,axiom,
    rdn_digit_add(rdnn(n6),rdnn(n7),rdnn(n3),rdnn(n1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n6_n7_n3_n1) ).

fof(f479,plain,
    sum(n6,n7,sK0),
    inference(cnf_transformation,[],[f475]) ).

fof(f475,plain,
    ( sK0 != sK1
    & sum(n7,n6,sK1)
    & sum(n6,n7,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f428,f474]) ).

fof(f474,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & sum(n7,n6,X1)
        & sum(n6,n7,X0) )
   => ( sK0 != sK1
      & sum(n7,n6,sK1)
      & sum(n6,n7,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f428,plain,
    ? [X0,X1] :
      ( X0 != X1
      & sum(n7,n6,X1)
      & sum(n6,n7,X0) ),
    inference(flattening,[],[f427]) ).

fof(f427,plain,
    ? [X0,X1] :
      ( X0 != X1
      & sum(n7,n6,X1)
      & sum(n6,n7,X0) ),
    inference(ennf_transformation,[],[f404]) ).

fof(f404,plain,
    ~ ! [X0,X1] :
        ( ( sum(n7,n6,X1)
          & sum(n6,n7,X0) )
       => X0 = X1 ),
    inference(rectify,[],[f403]) ).

fof(f403,negated_conjecture,
    ~ ! [X14,X15] :
        ( ( sum(n7,n6,X15)
          & sum(n6,n7,X14) )
       => X14 = X15 ),
    inference(negated_conjecture,[],[f402]) ).

fof(f402,conjecture,
    ! [X14,X15] :
      ( ( sum(n7,n6,X15)
        & sum(n6,n7,X14) )
     => X14 = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',communative_sum_n6_n7) ).

fof(f88637,plain,
    ~ sum(n7,n6,sK0),
    inference(unit_resulting_resolution,[],[f481,f480,f875]) ).

fof(f480,plain,
    sum(n7,n6,sK1),
    inference(cnf_transformation,[],[f475]) ).

fof(f481,plain,
    sK0 != sK1,
    inference(cnf_transformation,[],[f475]) ).

fof(f607,plain,
    rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,axiom,
    rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn13) ).

fof(f514,plain,
    rdn_translate(n6,rdn_pos(rdnn(n6))),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    rdn_translate(n6,rdn_pos(rdnn(n6))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn6) ).

fof(f515,plain,
    rdn_translate(n7,rdn_pos(rdnn(n7))),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    rdn_translate(n7,rdn_pos(rdnn(n7))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn7) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : NUM331+1 : TPTP v8.2.0. Released v3.1.0.
% 0.10/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon May 20 05:06:07 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.34  % (12936)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.37  % (12939)WARNING: value z3 for option sas not known
% 0.12/0.37  % (12940)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.37  % (12939)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)
% 0.12/0.37  % (12942)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)
% 0.12/0.37  % (12943)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)
% 0.12/0.37  % (12941)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)
% 0.12/0.37  % (12938)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.38  % (12937)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.40  TRYING [1]
% 0.12/0.40  TRYING [2]
% 0.18/0.45  TRYING [3]
% 0.18/0.46  TRYING [1]
% 0.18/0.47  TRYING [2]
% 0.18/0.56  TRYING [3]
% 2.15/0.68  TRYING [4]
% 4.23/0.96  TRYING [4]
% 7.76/1.48  TRYING [1]
% 7.76/1.49  TRYING [2]
% 8.12/1.52  TRYING [3]
% 9.12/1.66  TRYING [4]
% 11.01/1.93  TRYING [5]
% 16.18/2.69  TRYING [5]
% 30.68/4.74  TRYING [5]
% 55.26/8.28  TRYING [6]
% 59.54/8.87  TRYING [6]
% 108.22/15.84  % (12943)First to succeed.
% 108.22/15.85  % (12943)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12936"
% 108.39/15.87  % (12943)Refutation found. Thanks to Tanya!
% 108.39/15.87  % SZS status Theorem for theBenchmark
% 108.39/15.87  % SZS output start Proof for theBenchmark
% See solution above
% 108.39/15.87  % (12943)------------------------------
% 108.39/15.87  % (12943)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 108.39/15.87  % (12943)Termination reason: Refutation
% 108.39/15.87  
% 108.39/15.87  % (12943)Memory used [KB]: 124395
% 108.39/15.87  % (12943)Time elapsed: 15.488 s
% 108.39/15.87  % (12943)Instructions burned: 30497 (million)
% 108.39/15.87  % (12936)Success in time 15.515 s
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