TSTP Solution File: HEN010-2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : HEN010-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n026.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 : Fri Sep  1 15:58:48 EDT 2023

% Result   : Unsatisfiable 0.22s 0.55s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   45 (  24 unt;   0 def)
%            Number of atoms       :   93 (   3 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  107 (  59   ~;  43   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :  103 (; 103   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8458,plain,
    $false,
    inference(unit_resulting_resolution,[],[f3715,f7862,f7024,f35]) ).

fof(f35,plain,
    ! [X2,X0,X1,X7,X5] :
      ( ~ sP5(X1,X0,X2,X7)
      | ~ quotient(X0,X2,X5)
      | sP6(X7,X5,X2,X1) ),
    inference(cnf_transformation,[],[f35_D]) ).

fof(f35_D,plain,
    ! [X1,X2,X5,X7] :
      ( ! [X0] :
          ( ~ sP5(X1,X0,X2,X7)
          | ~ quotient(X0,X2,X5) )
    <=> ~ sP6(X7,X5,X2,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP6])]) ).

fof(f7024,plain,
    sP5(idQa,identity,idQ_idQa,zero),
    inference(unit_resulting_resolution,[],[f20,f12,f33]) ).

fof(f33,plain,
    ! [X2,X3,X0,X1,X7] :
      ( ~ quotient(X3,X2,X7)
      | ~ quotient(X0,X1,X3)
      | sP5(X1,X0,X2,X7) ),
    inference(cnf_transformation,[],[f33_D]) ).

fof(f33_D,plain,
    ! [X7,X2,X0,X1] :
      ( ! [X3] :
          ( ~ quotient(X3,X2,X7)
          | ~ quotient(X0,X1,X3) )
    <=> ~ sP5(X1,X0,X2,X7) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).

fof(f12,axiom,
    ! [X0] : quotient(X0,X0,zero),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',x_divide_x_is_zero) ).

fof(f20,axiom,
    quotient(identity,idQa,idQ_idQa),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',identity_divide_idQa) ).

fof(f7862,plain,
    ~ sP6(zero,idQa,idQ_idQa,idQa),
    inference(unit_resulting_resolution,[],[f21,f5480,f36]) ).

fof(f36,plain,
    ! [X2,X1,X7,X4,X5] :
      ( ~ sP6(X7,X5,X2,X1)
      | ~ sP4(X5,X4,X7)
      | ~ quotient(X1,X2,X4) ),
    inference(general_splitting,[],[f34,f35_D]) ).

fof(f34,plain,
    ! [X2,X0,X1,X7,X4,X5] :
      ( ~ quotient(X0,X2,X5)
      | ~ quotient(X1,X2,X4)
      | ~ sP4(X5,X4,X7)
      | ~ sP5(X1,X0,X2,X7) ),
    inference(general_splitting,[],[f32,f33_D]) ).

fof(f32,plain,
    ! [X2,X3,X0,X1,X7,X4,X5] :
      ( ~ quotient(X3,X2,X7)
      | ~ quotient(X0,X2,X5)
      | ~ quotient(X1,X2,X4)
      | ~ quotient(X0,X1,X3)
      | ~ sP4(X5,X4,X7) ),
    inference(general_splitting,[],[f4,f31_D]) ).

fof(f31,plain,
    ! [X6,X7,X4,X5] :
      ( ~ quotient(X5,X4,X6)
      | less_equal(X6,X7)
      | sP4(X5,X4,X7) ),
    inference(cnf_transformation,[],[f31_D]) ).

fof(f31_D,plain,
    ! [X7,X4,X5] :
      ( ! [X6] :
          ( ~ quotient(X5,X4,X6)
          | less_equal(X6,X7) )
    <=> ~ sP4(X5,X4,X7) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).

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/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',quotient_property) ).

fof(f5480,plain,
    sP4(idQa,idQa_Q__idQ_idQa,zero),
    inference(unit_resulting_resolution,[],[f2270,f8,f31]) ).

fof(f8,axiom,
    ! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',closure) ).

fof(f2270,plain,
    ~ less_equal(divide(idQa,idQa_Q__idQ_idQa),zero),
    inference(unit_resulting_resolution,[],[f13,f1734,f23]) ).

fof(f23,plain,
    ! [X2,X10,X0,X9] :
      ( ~ quotient(X0,X2,X10)
      | ~ less_equal(X9,X2)
      | sP0(X10,X0,X9) ),
    inference(cnf_transformation,[],[f23_D]) ).

fof(f23_D,plain,
    ! [X9,X0,X10] :
      ( ! [X2] :
          ( ~ quotient(X0,X2,X10)
          | ~ less_equal(X9,X2) )
    <=> ~ sP0(X10,X0,X9) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).

fof(f1734,plain,
    ! [X0] : ~ sP0(idQa,X0,divide(X0,idQa_Q__idQ_idQa)),
    inference(unit_resulting_resolution,[],[f101,f8,f24]) ).

fof(f24,plain,
    ! [X10,X0,X1,X9] :
      ( ~ sP0(X10,X0,X9)
      | ~ quotient(X0,X1,X9)
      | less_equal(X10,X1) ),
    inference(general_splitting,[],[f15,f23_D]) ).

fof(f15,axiom,
    ! [X2,X10,X0,X1,X9] :
      ( ~ less_equal(X9,X2)
      | less_equal(X10,X1)
      | ~ quotient(X0,X2,X10)
      | ~ quotient(X0,X1,X9) ),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',xQyLEz_implies_xQzLEy) ).

fof(f101,plain,
    ~ less_equal(idQa,idQa_Q__idQ_idQa),
    inference(unit_resulting_resolution,[],[f22,f70,f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',less_equal_and_equal) ).

fof(f70,plain,
    less_equal(idQa_Q__idQ_idQa,idQa),
    inference(unit_resulting_resolution,[],[f21,f3]) ).

fof(f3,axiom,
    ! [X2,X0,X1] :
      ( ~ quotient(X0,X1,X2)
      | less_equal(X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',divisor_existence) ).

fof(f22,axiom,
    idQa != idQa_Q__idQ_idQa,
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',prove_idQa_equals_idQa_Q__idQ_idQa) ).

fof(f13,axiom,
    ! [X0] : quotient(X0,zero,X0),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',x_divde_zero_is_x) ).

fof(f21,axiom,
    quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',identity_divide_idQ_idQa) ).

fof(f3715,plain,
    quotient(identity,idQ_idQa,idQa),
    inference(superposition,[],[f8,f3524]) ).

fof(f3524,plain,
    idQa = divide(identity,idQ_idQa),
    inference(unit_resulting_resolution,[],[f1820,f3423,f6]) ).

fof(f3423,plain,
    less_equal(idQa,divide(identity,idQ_idQa)),
    inference(unit_resulting_resolution,[],[f8,f2885,f25]) ).

fof(f25,plain,
    ! [X2,X10,X0,X9] :
      ( ~ quotient(X2,X0,X10)
      | less_equal(X9,X10)
      | sP1(X2,X0,X9) ),
    inference(cnf_transformation,[],[f25_D]) ).

fof(f25_D,plain,
    ! [X9,X0,X2] :
      ( ! [X10] :
          ( ~ quotient(X2,X0,X10)
          | less_equal(X9,X10) )
    <=> ~ sP1(X2,X0,X9) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).

fof(f2885,plain,
    ~ sP1(identity,idQ_idQa,idQa),
    inference(unit_resulting_resolution,[],[f1894,f19,f26]) ).

fof(f26,plain,
    ! [X2,X0,X1,X9] :
      ( ~ sP1(X2,X0,X9)
      | ~ quotient(X2,X1,X9)
      | ~ less_equal(X0,X1) ),
    inference(general_splitting,[],[f16,f25_D]) ).

fof(f16,axiom,
    ! [X2,X10,X0,X1,X9] :
      ( ~ less_equal(X0,X1)
      | less_equal(X9,X10)
      | ~ quotient(X2,X0,X10)
      | ~ quotient(X2,X1,X9) ),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',xLEy_implies_zQyLEzQx) ).

fof(f19,axiom,
    quotient(identity,a,idQa),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',identity_divide_a) ).

fof(f1894,plain,
    less_equal(idQ_idQa,a),
    inference(unit_resulting_resolution,[],[f19,f1576,f24]) ).

fof(f1576,plain,
    sP0(idQ_idQa,identity,idQa),
    inference(unit_resulting_resolution,[],[f54,f20,f23]) ).

fof(f54,plain,
    ! [X0] : less_equal(X0,X0),
    inference(unit_resulting_resolution,[],[f12,f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ~ quotient(X0,X1,zero)
      | less_equal(X0,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.zCc5F2kNSI/Vampire---4.8_3830',less_equal_quotient) ).

fof(f1820,plain,
    less_equal(divide(identity,idQ_idQa),idQa),
    inference(unit_resulting_resolution,[],[f20,f1552,f24]) ).

fof(f1552,plain,
    ! [X0,X1] : sP0(divide(X0,X1),X0,X1),
    inference(unit_resulting_resolution,[],[f54,f8,f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : HEN010-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37  % Computer : n026.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Wed Aug 30 14:53:36 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.22/0.43  % (4102)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (4133)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.43  % (4132)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.43  % (4135)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43  % (4134)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 Vampire---4 for (569ds/0Mi)
% 0.22/0.43  % (4136)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 Vampire---4 for (531ds/0Mi)
% 0.22/0.43  % (4137)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 Vampire---4 for (522ds/0Mi)
% 0.22/0.43  % (4138)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 Vampire---4 for (497ds/0Mi)
% 0.22/0.43  TRYING [1]
% 0.22/0.44  TRYING [2]
% 0.22/0.44  TRYING [3]
% 0.22/0.44  TRYING [1]
% 0.22/0.44  TRYING [2]
% 0.22/0.44  TRYING [4]
% 0.22/0.45  TRYING [3]
% 0.22/0.45  TRYING [5]
% 0.22/0.46  TRYING [4]
% 0.22/0.48  TRYING [6]
% 0.22/0.51  TRYING [5]
% 0.22/0.55  TRYING [7]
% 0.22/0.55  % (4138)First to succeed.
% 0.22/0.55  % (4138)Refutation found. Thanks to Tanya!
% 0.22/0.55  % SZS status Unsatisfiable for Vampire---4
% 0.22/0.55  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.55  % (4138)------------------------------
% 0.22/0.55  % (4138)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.55  % (4138)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.55  % (4138)Termination reason: Refutation
% 0.22/0.55  
% 0.22/0.55  % (4138)Memory used [KB]: 3326
% 0.22/0.55  % (4138)Time elapsed: 0.118 s
% 0.22/0.55  % (4138)------------------------------
% 0.22/0.55  % (4138)------------------------------
% 0.22/0.55  % (4102)Success in time 0.179 s
% 0.22/0.55  % Vampire---4.8 exiting
%------------------------------------------------------------------------------