TSTP Solution File: KLE048+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE048+1 : 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 : n007.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 13:11:47 EDT 2024

% Result   : Theorem 0.20s 0.57s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   67 (  41 unt;   0 def)
%            Number of atoms       :  119 (  59 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :   82 (  30   ~;  23   |;  18   &)
%                                         (   5 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   90 (  83   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12674,plain,
    $false,
    inference(subsumption_resolution,[],[f12673,f45]) ).

fof(f45,plain,
    one != star(sK0),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ( one != star(sK0)
    & test(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f29,f34]) ).

fof(f34,plain,
    ( ? [X0] :
        ( one != star(X0)
        & test(X0) )
   => ( one != star(sK0)
      & test(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ? [X0] :
      ( one != star(X0)
      & test(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ~ ! [X0] :
        ( test(X0)
       => one = star(X0) ),
    inference(rectify,[],[f22]) ).

fof(f22,negated_conjecture,
    ~ ! [X3] :
        ( test(X3)
       => one = star(X3) ),
    inference(negated_conjecture,[],[f21]) ).

fof(f21,conjecture,
    ! [X3] :
      ( test(X3)
     => one = star(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f12673,plain,
    one = star(sK0),
    inference(forward_demodulation,[],[f12671,f10829]) ).

fof(f10829,plain,
    one = addition(one,star(sK0)),
    inference(superposition,[],[f10826,f57]) ).

fof(f57,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(f10826,plain,
    one = addition(star(sK0),one),
    inference(unit_resulting_resolution,[],[f10825,f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ( leq(X0,X1)
        | addition(X0,X1) != X1 )
      & ( addition(X0,X1) = X1
        | ~ leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

fof(f10825,plain,
    leq(star(sK0),one),
    inference(superposition,[],[f10804,f50]) ).

fof(f50,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(f10804,plain,
    ! [X0] : leq(multiplication(X0,star(sK0)),X0),
    inference(subsumption_resolution,[],[f10768,f156]) ).

fof(f156,plain,
    ! [X0] : leq(X0,X0),
    inference(unit_resulting_resolution,[],[f51,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f51,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',additive_idempotence) ).

fof(f10768,plain,
    ! [X0] :
      ( ~ leq(X0,X0)
      | leq(multiplication(X0,star(sK0)),X0) ),
    inference(superposition,[],[f70,f5624]) ).

fof(f5624,plain,
    ! [X0] : addition(multiplication(X0,sK0),X0) = X0,
    inference(unit_resulting_resolution,[],[f5616,f64]) ).

fof(f5616,plain,
    ! [X0] : leq(multiplication(X0,sK0),X0),
    inference(forward_demodulation,[],[f5592,f49]) ).

fof(f49,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(f5592,plain,
    ! [X0] : leq(multiplication(X0,sK0),multiplication(X0,one)),
    inference(superposition,[],[f3703,f319]) ).

fof(f319,plain,
    one = addition(sK0,one),
    inference(superposition,[],[f282,f135]) ).

fof(f135,plain,
    one = addition(sK0,sK1(sK0)),
    inference(unit_resulting_resolution,[],[f73,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ complement(X1,X0)
      | addition(X0,X1) = one ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( addition(X0,X1) = one
        & zero = multiplication(X1,X0)
        & zero = multiplication(X0,X1) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X3,X4] :
      ( complement(X4,X3)
    <=> ( one = addition(X3,X4)
        & zero = multiplication(X4,X3)
        & zero = multiplication(X3,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).

fof(f73,plain,
    complement(sK1(sK0),sK0),
    inference(unit_resulting_resolution,[],[f44,f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ test(X0)
      | complement(sK1(X0),X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( complement(sK1(X0),X0)
        | ~ test(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f37,f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ? [X2] : complement(X2,X0)
     => complement(sK1(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X2] : complement(X2,X0)
        | ~ test(X0) ) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X1] : complement(X1,X0)
        | ~ test(X0) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0] :
      ( test(X0)
    <=> ? [X1] : complement(X1,X0) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X3] :
      ( test(X3)
    <=> ? [X4] : complement(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).

fof(f44,plain,
    test(sK0),
    inference(cnf_transformation,[],[f35]) ).

fof(f282,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
    inference(superposition,[],[f66,f51]) ).

fof(f66,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,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(f3703,plain,
    ! [X2,X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
    inference(superposition,[],[f306,f68]) ).

fof(f68,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/sandbox/benchmark/theBenchmark.p',right_distributivity) ).

fof(f306,plain,
    ! [X0,X1] : leq(X0,addition(X0,X1)),
    inference(unit_resulting_resolution,[],[f282,f65]) ).

fof(f70,plain,
    ! [X2,X0,X1] :
      ( ~ leq(addition(multiplication(X0,X1),X2),X0)
      | leq(multiplication(X2,star(X1)),X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( leq(multiplication(X2,star(X1)),X0)
      | ~ leq(addition(multiplication(X0,X1),X2),X0) ),
    inference(ennf_transformation,[],[f16]) ).

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

fof(f12671,plain,
    star(sK0) = addition(one,star(sK0)),
    inference(unit_resulting_resolution,[],[f12540,f64]) ).

fof(f12540,plain,
    leq(one,star(sK0)),
    inference(superposition,[],[f52,f11936]) ).

fof(f11936,plain,
    one = addition(one,multiplication(sK0,star(sK0))),
    inference(forward_demodulation,[],[f11857,f332]) ).

fof(f332,plain,
    one = addition(one,sK0),
    inference(superposition,[],[f319,f57]) ).

fof(f11857,plain,
    addition(one,sK0) = addition(one,multiplication(sK0,star(sK0))),
    inference(superposition,[],[f1059,f10821]) ).

fof(f10821,plain,
    ! [X0] : addition(multiplication(X0,star(sK0)),X0) = X0,
    inference(unit_resulting_resolution,[],[f10804,f64]) ).

fof(f1059,plain,
    ! [X0] : addition(one,X0) = addition(one,addition(X0,sK0)),
    inference(superposition,[],[f346,f57]) ).

fof(f346,plain,
    ! [X0] : addition(one,X0) = addition(one,addition(sK0,X0)),
    inference(superposition,[],[f66,f332]) ).

fof(f52,plain,
    ! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : KLE048+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % 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   : Tue Apr 30 04:54:48 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (10196)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (10200)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [3]
% 0.14/0.37  % (10199)WARNING: value z3 for option sas not known
% 0.14/0.37  % (10197)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (10198)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (10201)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)
% 0.14/0.37  % (10203)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)
% 0.14/0.37  % (10199)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)
% 0.14/0.37  % (10202)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)
% 0.14/0.37  TRYING [4]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.39  TRYING [5]
% 0.14/0.40  TRYING [3]
% 0.20/0.45  TRYING [4]
% 0.20/0.46  TRYING [6]
% 0.20/0.57  % (10203)First to succeed.
% 0.20/0.57  % (10203)Refutation found. Thanks to Tanya!
% 0.20/0.57  % SZS status Theorem for theBenchmark
% 0.20/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.57  % (10203)------------------------------
% 0.20/0.57  % (10203)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.57  % (10203)Termination reason: Refutation
% 0.20/0.57  
% 0.20/0.57  % (10203)Memory used [KB]: 2792
% 0.20/0.57  % (10203)Time elapsed: 0.201 s
% 0.20/0.57  % (10203)Instructions burned: 303 (million)
% 0.20/0.57  % (10203)------------------------------
% 0.20/0.57  % (10203)------------------------------
% 0.20/0.57  % (10196)Success in time 0.203 s
%------------------------------------------------------------------------------