TSTP Solution File: HEN008-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : HEN008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 06:11:55 EDT 2024

% Result   : Unsatisfiable 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   35 (  20 unt;   0 def)
%            Number of atoms       :   68 (   5 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   74 (  41   ~;  30   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   75 (  75   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f524,plain,
    $false,
    inference(subsumption_resolution,[],[f515,f26]) ).

fof(f26,plain,
    ~ quotient(aQc,bQc,zero),
    inference(unit_resulting_resolution,[],[f13,f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ~ quotient(X0,X1,zero)
      | less_equal(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_quotient) ).

fof(f13,axiom,
    ~ less_equal(aQc,bQc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).

fof(f515,plain,
    quotient(aQc,bQc,zero),
    inference(superposition,[],[f8,f508]) ).

fof(f508,plain,
    zero = divide(aQc,bQc),
    inference(unit_resulting_resolution,[],[f5,f500,f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).

fof(f500,plain,
    less_equal(divide(aQc,bQc),zero),
    inference(unit_resulting_resolution,[],[f8,f498,f14]) ).

fof(f14,plain,
    ! [X6,X7,X4,X5] :
      ( ~ quotient(X5,X4,X6)
      | less_equal(X6,X7)
      | sP0(X5,X4,X7) ),
    inference(cnf_transformation,[],[f14_D]) ).

fof(f14_D,plain,
    ! [X7,X4,X5] :
      ( ! [X6] :
          ( ~ quotient(X5,X4,X6)
          | less_equal(X6,X7) )
    <=> ~ sP0(X5,X4,X7) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).

fof(f498,plain,
    ~ sP0(aQc,bQc,zero),
    inference(forward_demodulation,[],[f496,f115]) ).

fof(f115,plain,
    bQc = divide(b,c),
    inference(unit_resulting_resolution,[],[f8,f12,f9]) ).

fof(f9,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ quotient(X0,X1,X8)
      | X2 = X8
      | ~ quotient(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined) ).

fof(f12,axiom,
    quotient(b,c,bQc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).

fof(f496,plain,
    ~ sP0(aQc,divide(b,c),zero),
    inference(unit_resulting_resolution,[],[f8,f374,f19]) ).

fof(f19,plain,
    ! [X2,X1,X7,X4,X5] :
      ( ~ sP2(X7,X5,X2,X1)
      | ~ sP0(X5,X4,X7)
      | ~ quotient(X1,X2,X4) ),
    inference(general_splitting,[],[f17,f18_D]) ).

fof(f18,plain,
    ! [X2,X0,X1,X7,X5] :
      ( ~ sP1(X1,X0,X2,X7)
      | ~ quotient(X0,X2,X5)
      | sP2(X7,X5,X2,X1) ),
    inference(cnf_transformation,[],[f18_D]) ).

fof(f18_D,plain,
    ! [X1,X2,X5,X7] :
      ( ! [X0] :
          ( ~ sP1(X1,X0,X2,X7)
          | ~ quotient(X0,X2,X5) )
    <=> ~ sP2(X7,X5,X2,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).

fof(f17,plain,
    ! [X2,X0,X1,X7,X4,X5] :
      ( ~ quotient(X0,X2,X5)
      | ~ quotient(X1,X2,X4)
      | ~ sP0(X5,X4,X7)
      | ~ sP1(X1,X0,X2,X7) ),
    inference(general_splitting,[],[f15,f16_D]) ).

fof(f16,plain,
    ! [X2,X3,X0,X1,X7] :
      ( ~ quotient(X3,X2,X7)
      | ~ quotient(X0,X1,X3)
      | sP1(X1,X0,X2,X7) ),
    inference(cnf_transformation,[],[f16_D]) ).

fof(f16_D,plain,
    ! [X7,X2,X0,X1] :
      ( ! [X3] :
          ( ~ quotient(X3,X2,X7)
          | ~ quotient(X0,X1,X3) )
    <=> ~ sP1(X1,X0,X2,X7) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).

fof(f15,plain,
    ! [X2,X3,X0,X1,X7,X4,X5] :
      ( ~ quotient(X3,X2,X7)
      | ~ quotient(X0,X2,X5)
      | ~ quotient(X1,X2,X4)
      | ~ quotient(X0,X1,X3)
      | ~ sP0(X5,X4,X7) ),
    inference(general_splitting,[],[f4,f14_D]) ).

fof(f4,axiom,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( less_equal(X6,X7)
      | ~ quotient(X3,X2,X7)
      | ~ quotient(X5,X4,X6)
      | ~ quotient(X0,X2,X5)
      | ~ quotient(X1,X2,X4)
      | ~ quotient(X0,X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).

fof(f374,plain,
    sP2(zero,aQc,c,b),
    inference(unit_resulting_resolution,[],[f11,f282,f18]) ).

fof(f282,plain,
    ! [X0] : sP1(b,a,X0,zero),
    inference(forward_demodulation,[],[f257,f68]) ).

fof(f68,plain,
    ! [X0] : zero = divide(zero,X0),
    inference(unit_resulting_resolution,[],[f5,f36,f6]) ).

fof(f36,plain,
    ! [X0,X1] : less_equal(divide(X0,X1),X0),
    inference(unit_resulting_resolution,[],[f8,f3]) ).

fof(f3,axiom,
    ! [X2,X0,X1] :
      ( ~ quotient(X0,X1,X2)
      | less_equal(X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_existence) ).

fof(f257,plain,
    ! [X0] : sP1(b,a,X0,divide(zero,X0)),
    inference(unit_resulting_resolution,[],[f20,f8,f16]) ).

fof(f20,plain,
    quotient(a,b,zero),
    inference(unit_resulting_resolution,[],[f10,f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | quotient(X0,X1,zero) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal) ).

fof(f10,axiom,
    less_equal(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aLEb) ).

fof(f11,axiom,
    quotient(a,c,aQc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).

fof(f5,axiom,
    ! [X0] : less_equal(zero,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).

fof(f8,axiom,
    ! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : HEN008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n018.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   : Fri May  3 13:04:02 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (19659)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (19664)WARNING: value z3 for option sas not known
% 0.14/0.38  % (19663)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (19662)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (19666)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)
% 0.14/0.38  % (19667)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)
% 0.14/0.38  % (19664)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)
% 0.14/0.38  % (19668)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)
% 0.14/0.38  % (19665)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [3]
% 0.14/0.39  % (19668)First to succeed.
% 0.14/0.39  % (19668)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19659"
% 0.14/0.39  % (19668)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (19668)------------------------------
% 0.14/0.39  % (19668)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (19668)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (19668)Memory used [KB]: 885
% 0.14/0.39  % (19668)Time elapsed: 0.012 s
% 0.14/0.39  % (19668)Instructions burned: 16 (million)
% 0.14/0.39  % (19659)Success in time 0.028 s
%------------------------------------------------------------------------------