TSTP Solution File: KLE144+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE144+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 Apr 30 13:12:02 EDT 2024

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   76 (  32 unt;   0 def)
%            Number of atoms       :  124 (  44 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   88 (  40   ~;  34   |;   4   &)
%                                         (   7 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   7 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  103 ( 101   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4846,plain,
    $false,
    inference(avatar_sat_refutation,[],[f157,f295,f558,f836,f4845]) ).

fof(f4845,plain,
    spl1_2,
    inference(avatar_contradiction_clause,[],[f4843]) ).

fof(f4843,plain,
    ( $false
    | spl1_2 ),
    inference(resolution,[],[f4624,f156]) ).

fof(f156,plain,
    ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
    | spl1_2 ),
    inference(avatar_component_clause,[],[f154]) ).

fof(f154,plain,
    ( spl1_2
  <=> leq(strong_iteration(one),strong_iteration(star(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

fof(f4624,plain,
    ! [X0,X1] : leq(X1,strong_iteration(star(X0))),
    inference(superposition,[],[f4618,f36]) ).

fof(f36,plain,
    ! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).

fof(f4618,plain,
    ! [X0,X1] : leq(X1,strong_iteration(addition(one,X0))),
    inference(superposition,[],[f4505,f33]) ).

fof(f33,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

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

fof(f4505,plain,
    ! [X2,X0,X1] : leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)),
    inference(subsumption_resolution,[],[f4504,f356]) ).

fof(f356,plain,
    ! [X0,X1] : leq(X0,addition(X0,X1)),
    inference(trivial_inequality_removal,[],[f350]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != addition(X0,X1)
      | leq(X0,addition(X0,X1)) ),
    inference(superposition,[],[f42,f180]) ).

fof(f180,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
    inference(superposition,[],[f43,f35]) ).

fof(f35,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

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

fof(f43,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,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/sandbox/benchmark/theBenchmark.p',additive_associativity) ).

fof(f42,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( leq(X0,X1)
        | addition(X0,X1) != X1 )
      & ( addition(X0,X1) = X1
        | ~ leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

fof(f4504,plain,
    ! [X2,X0,X1] :
      ( ~ leq(X1,addition(X1,addition(multiplication(X0,X1),X2)))
      | leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)) ),
    inference(forward_demodulation,[],[f4404,f43]) ).

fof(f4404,plain,
    ! [X2,X0,X1] :
      ( ~ leq(X1,addition(addition(X1,multiplication(X0,X1)),X2))
      | leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)) ),
    inference(superposition,[],[f47,f431]) ).

fof(f431,plain,
    ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
    inference(superposition,[],[f46,f34]) ).

fof(f34,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

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

fof(f46,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( ~ leq(X2,addition(multiplication(X0,X2),X1))
      | leq(X2,multiplication(strong_iteration(X0),X1)) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( leq(X2,multiplication(strong_iteration(X0),X1))
      | ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1,X2] :
      ( leq(X2,addition(multiplication(X0,X2),X1))
     => leq(X2,multiplication(strong_iteration(X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).

fof(f836,plain,
    ( ~ spl1_5
    | spl1_6 ),
    inference(avatar_split_clause,[],[f826,f834,f830]) ).

fof(f830,plain,
    ( spl1_5
  <=> leq(one,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

fof(f834,plain,
    ( spl1_6
  <=> ! [X0] : leq(star(X0),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).

fof(f826,plain,
    ! [X0] :
      ( leq(star(X0),zero)
      | ~ leq(one,zero) ),
    inference(superposition,[],[f656,f34]) ).

fof(f656,plain,
    ! [X0,X1] :
      ( leq(multiplication(X1,star(X0)),zero)
      | ~ leq(X1,zero) ),
    inference(forward_demodulation,[],[f639,f50]) ).

fof(f50,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(superposition,[],[f40,f32]) ).

fof(f32,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

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

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/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f639,plain,
    ! [X0,X1] :
      ( ~ leq(addition(zero,X1),zero)
      | leq(multiplication(X1,star(X0)),zero) ),
    inference(superposition,[],[f48,f31]) ).

fof(f31,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(cnf_transformation,[],[f10]) ).

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

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ leq(addition(multiplication(X2,X0),X1),X2)
      | leq(multiplication(X1,star(X0)),X2) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( leq(multiplication(X1,star(X0)),X2)
      | ~ leq(addition(multiplication(X2,X0),X1),X2) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( leq(addition(multiplication(X2,X0),X1),X2)
     => leq(multiplication(X1,star(X0)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction2) ).

fof(f558,plain,
    spl1_1,
    inference(avatar_contradiction_clause,[],[f557]) ).

fof(f557,plain,
    ( $false
    | spl1_1 ),
    inference(resolution,[],[f555,f152]) ).

fof(f152,plain,
    ( ~ leq(strong_iteration(star(sK0)),strong_iteration(one))
    | spl1_1 ),
    inference(avatar_component_clause,[],[f150]) ).

fof(f150,plain,
    ( spl1_1
  <=> leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

fof(f555,plain,
    ! [X0] : leq(X0,strong_iteration(one)),
    inference(superposition,[],[f551,f33]) ).

fof(f551,plain,
    ! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
    inference(subsumption_resolution,[],[f536,f356]) ).

fof(f536,plain,
    ! [X0,X1] :
      ( ~ leq(X0,addition(X0,X1))
      | leq(X0,multiplication(strong_iteration(one),X1)) ),
    inference(superposition,[],[f47,f34]) ).

fof(f295,plain,
    ( ~ spl1_3
    | spl1_4 ),
    inference(avatar_split_clause,[],[f285,f292,f288]) ).

fof(f288,plain,
    ( spl1_3
  <=> zero = star(one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

fof(f292,plain,
    ( spl1_4
  <=> zero = one ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

fof(f285,plain,
    ( zero = one
    | zero != star(one) ),
    inference(inner_rewriting,[],[f265]) ).

fof(f265,plain,
    ( one = star(one)
    | zero != star(one) ),
    inference(superposition,[],[f213,f67]) ).

fof(f67,plain,
    star(one) = addition(one,star(one)),
    inference(superposition,[],[f36,f34]) ).

fof(f213,plain,
    ! [X0,X1] :
      ( addition(X1,X0) = X1
      | zero != X0 ),
    inference(superposition,[],[f206,f40]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = X1
      | zero != X0 ),
    inference(forward_demodulation,[],[f178,f50]) ).

fof(f178,plain,
    ! [X0,X1] :
      ( addition(zero,X1) = addition(X0,addition(zero,X1))
      | zero != X0 ),
    inference(superposition,[],[f43,f74]) ).

fof(f74,plain,
    ! [X0] :
      ( zero = addition(X0,zero)
      | zero != X0 ),
    inference(resolution,[],[f58,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f58,plain,
    ! [X0] :
      ( leq(X0,zero)
      | zero != X0 ),
    inference(superposition,[],[f42,f32]) ).

fof(f157,plain,
    ( ~ spl1_1
    | ~ spl1_2 ),
    inference(avatar_split_clause,[],[f30,f154,f150]) ).

fof(f30,plain,
    ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
    | ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
    | ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f27]) ).

fof(f27,plain,
    ( ? [X0] :
        ( ~ leq(strong_iteration(one),strong_iteration(star(X0)))
        | ~ leq(strong_iteration(star(X0)),strong_iteration(one)) )
   => ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
      | ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0] :
      ( ~ leq(strong_iteration(one),strong_iteration(star(X0)))
      | ~ leq(strong_iteration(star(X0)),strong_iteration(one)) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ! [X0] :
        ( leq(strong_iteration(one),strong_iteration(star(X0)))
        & leq(strong_iteration(star(X0)),strong_iteration(one)) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X3] :
        ( leq(strong_iteration(one),strong_iteration(star(X3)))
        & leq(strong_iteration(star(X3)),strong_iteration(one)) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X3] :
      ( leq(strong_iteration(one),strong_iteration(star(X3)))
      & leq(strong_iteration(star(X3)),strong_iteration(one)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : KLE144+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n017.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   : Tue Apr 30 04:32:48 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (1638)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (1641)WARNING: value z3 for option sas not known
% 0.13/0.36  % (1641)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)
% 0.13/0.36  % (1640)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (1644)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)
% 0.13/0.36  % (1645)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)
% 0.13/0.36  % (1642)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (1643)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)
% 0.13/0.36  TRYING [1]
% 0.13/0.36  TRYING [2]
% 0.13/0.36  % (1639)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  TRYING [3]
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2]
% 0.13/0.37  TRYING [4]
% 0.13/0.39  TRYING [3]
% 0.19/0.41  TRYING [5]
% 0.19/0.42  TRYING [4]
% 0.19/0.46  % (1641)First to succeed.
% 0.19/0.47  % (1641)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Theorem for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47  % (1641)------------------------------
% 0.19/0.47  % (1641)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.47  % (1641)Termination reason: Refutation
% 0.19/0.47  
% 0.19/0.47  % (1641)Memory used [KB]: 2180
% 0.19/0.47  % (1641)Time elapsed: 0.106 s
% 0.19/0.47  % (1641)Instructions burned: 233 (million)
% 0.19/0.47  % (1641)------------------------------
% 0.19/0.47  % (1641)------------------------------
% 0.19/0.47  % (1638)Success in time 0.12 s
%------------------------------------------------------------------------------