TSTP Solution File: KLE056+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE056+1 : TPTP v8.2.0. Released v4.0.0.
% 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 : Mon May 20 23:15:21 EDT 2024

% Result   : Theorem 0.07s 0.30s
% Output   : Refutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   90 (  55 unt;   0 def)
%            Number of atoms       :  138 (  78 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   78 (  30   ~;  22   |;   4   &)
%                                         (  18 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   20 (  18 usr;  19 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   90 (  88   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f205,plain,
    $false,
    inference(avatar_sat_refutation,[],[f51,f56,f61,f65,f69,f73,f77,f81,f85,f89,f95,f107,f111,f115,f146,f150,f154,f203,f204]) ).

fof(f204,plain,
    ( spl1_1
    | ~ spl1_2
    | ~ spl1_5
    | ~ spl1_6
    | ~ spl1_15 ),
    inference(avatar_split_clause,[],[f161,f144,f71,f67,f53,f48]) ).

fof(f48,plain,
    ( spl1_1
  <=> zero = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

fof(f53,plain,
    ( spl1_2
  <=> zero = domain(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

fof(f67,plain,
    ( spl1_5
  <=> ! [X0] : zero = multiplication(zero,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

fof(f71,plain,
    ( spl1_6
  <=> ! [X0] : addition(X0,zero) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).

fof(f144,plain,
    ( spl1_15
  <=> ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).

fof(f161,plain,
    ( zero = sK0
    | ~ spl1_2
    | ~ spl1_5
    | ~ spl1_6
    | ~ spl1_15 ),
    inference(forward_demodulation,[],[f160,f72]) ).

fof(f72,plain,
    ( ! [X0] : addition(X0,zero) = X0
    | ~ spl1_6 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f160,plain,
    ( zero = addition(sK0,zero)
    | ~ spl1_2
    | ~ spl1_5
    | ~ spl1_15 ),
    inference(forward_demodulation,[],[f155,f68]) ).

fof(f68,plain,
    ( ! [X0] : zero = multiplication(zero,X0)
    | ~ spl1_5 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f155,plain,
    ( multiplication(zero,sK0) = addition(sK0,multiplication(zero,sK0))
    | ~ spl1_2
    | ~ spl1_15 ),
    inference(superposition,[],[f145,f55]) ).

fof(f55,plain,
    ( zero = domain(sK0)
    | ~ spl1_2 ),
    inference(avatar_component_clause,[],[f53]) ).

fof(f145,plain,
    ( ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0))
    | ~ spl1_15 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f203,plain,
    spl1_18,
    inference(avatar_split_clause,[],[f45,f201]) ).

fof(f201,plain,
    ( spl1_18
  <=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).

fof(f45,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).

fof(f154,plain,
    spl1_17,
    inference(avatar_split_clause,[],[f44,f152]) ).

fof(f152,plain,
    ( spl1_17
  <=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).

fof(f44,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).

fof(f150,plain,
    spl1_16,
    inference(avatar_split_clause,[],[f43,f148]) ).

fof(f148,plain,
    ( spl1_16
  <=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).

fof(f43,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).

fof(f146,plain,
    spl1_15,
    inference(avatar_split_clause,[],[f39,f144]) ).

fof(f39,plain,
    ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3] : multiplication(domain(X3),X3) = addition(X3,multiplication(domain(X3),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).

fof(f115,plain,
    spl1_14,
    inference(avatar_split_clause,[],[f42,f113]) ).

fof(f113,plain,
    ( spl1_14
  <=> ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).

fof(f42,plain,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3,X4] : domain(multiplication(X3,X4)) = domain(multiplication(X3,domain(X4))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).

fof(f111,plain,
    ( spl1_13
    | ~ spl1_6
    | ~ spl1_11 ),
    inference(avatar_split_clause,[],[f96,f93,f71,f109]) ).

fof(f109,plain,
    ( spl1_13
  <=> ! [X0] : addition(zero,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).

fof(f93,plain,
    ( spl1_11
  <=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).

fof(f96,plain,
    ( ! [X0] : addition(zero,X0) = X0
    | ~ spl1_6
    | ~ spl1_11 ),
    inference(superposition,[],[f94,f72]) ).

fof(f94,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
    | ~ spl1_11 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f107,plain,
    spl1_12,
    inference(avatar_split_clause,[],[f41,f105]) ).

fof(f105,plain,
    ( spl1_12
  <=> ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).

fof(f41,plain,
    ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X3,X4] : domain(addition(X3,X4)) = addition(domain(X3),domain(X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).

fof(f95,plain,
    spl1_11,
    inference(avatar_split_clause,[],[f40,f93]) ).

fof(f40,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f89,plain,
    spl1_10,
    inference(avatar_split_clause,[],[f38,f87]) ).

fof(f87,plain,
    ( spl1_10
  <=> ! [X0] : one = addition(domain(X0),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).

fof(f38,plain,
    ! [X0] : one = addition(domain(X0),one),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0] : one = addition(domain(X0),one),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3] : one = addition(domain(X3),one),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).

fof(f85,plain,
    spl1_9,
    inference(avatar_split_clause,[],[f37,f83]) ).

fof(f83,plain,
    ( spl1_9
  <=> ! [X0] : addition(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).

fof(f37,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f81,plain,
    spl1_8,
    inference(avatar_split_clause,[],[f36,f79]) ).

fof(f79,plain,
    ( spl1_8
  <=> ! [X0] : multiplication(one,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).

fof(f36,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

fof(f77,plain,
    spl1_7,
    inference(avatar_split_clause,[],[f35,f75]) ).

fof(f75,plain,
    ( spl1_7
  <=> ! [X0] : multiplication(X0,one) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).

fof(f35,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).

fof(f73,plain,
    spl1_6,
    inference(avatar_split_clause,[],[f34,f71]) ).

fof(f34,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).

fof(f69,plain,
    spl1_5,
    inference(avatar_split_clause,[],[f33,f67]) ).

fof(f33,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] : zero = multiplication(zero,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).

fof(f65,plain,
    spl1_4,
    inference(avatar_split_clause,[],[f32,f63]) ).

fof(f63,plain,
    ( spl1_4
  <=> ! [X0] : zero = multiplication(X0,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

fof(f32,plain,
    ! [X0] : zero = multiplication(X0,zero),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] : zero = multiplication(X0,zero),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).

fof(f61,plain,
    spl1_3,
    inference(avatar_split_clause,[],[f31,f58]) ).

fof(f58,plain,
    ( spl1_3
  <=> zero = domain(zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

fof(f31,plain,
    zero = domain(zero),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    zero = domain(zero),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).

fof(f56,plain,
    spl1_2,
    inference(avatar_split_clause,[],[f29,f53]) ).

fof(f29,plain,
    zero = domain(sK0),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( zero != sK0
    & zero = domain(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f26,f27]) ).

fof(f27,plain,
    ( ? [X0] :
        ( zero != X0
        & zero = domain(X0) )
   => ( zero != sK0
      & zero = domain(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0] :
      ( zero != X0
      & zero = domain(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ! [X0] :
        ( zero = domain(X0)
       => zero = X0 ),
    inference(rectify,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ! [X3] :
        ( zero = domain(X3)
       => zero = X3 ),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ! [X3] :
      ( zero = domain(X3)
     => zero = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f51,plain,
    ~ spl1_1,
    inference(avatar_split_clause,[],[f30,f48]) ).

fof(f30,plain,
    zero != sK0,
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : KLE056+1 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.28  % Computer : n011.cluster.edu
% 0.07/0.28  % Model    : x86_64 x86_64
% 0.07/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28  % Memory   : 8042.1875MB
% 0.07/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28  % CPULimit   : 300
% 0.07/0.28  % WCLimit    : 300
% 0.07/0.28  % DateTime   : Sun May 19 09:57:07 EDT 2024
% 0.07/0.28  % CPUTime    : 
% 0.07/0.28  % (3880)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.29  % (3883)WARNING: value z3 for option sas not known
% 0.07/0.30  % (3882)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.30  % (3885)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)
% 0.07/0.30  % (3886)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)
% 0.07/0.30  % (3883)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)
% 0.07/0.30  % (3888)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)
% 0.07/0.30  % (3884)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.30  TRYING [1]
% 0.07/0.30  % (3881)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.30  TRYING [2]
% 0.07/0.30  TRYING [3]
% 0.07/0.30  % (3885)First to succeed.
% 0.07/0.30  % (3885)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3880"
% 0.07/0.30  TRYING [1]
% 0.07/0.30  TRYING [2]
% 0.07/0.30  % (3885)Refutation found. Thanks to Tanya!
% 0.07/0.30  % SZS status Theorem for theBenchmark
% 0.07/0.30  % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.30  % (3885)------------------------------
% 0.07/0.30  % (3885)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.07/0.30  % (3885)Termination reason: Refutation
% 0.07/0.30  
% 0.07/0.30  % (3885)Memory used [KB]: 891
% 0.07/0.30  % (3885)Time elapsed: 0.007 s
% 0.07/0.30  % (3885)Instructions burned: 10 (million)
% 0.07/0.30  % (3880)Success in time 0.021 s
%------------------------------------------------------------------------------