%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n014.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 : Wed Aug 31 16:19:12 EDT 2022

% Result   : Unsatisfiable 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   36 (  12 unt;   0 def)
%            Number of atoms       :   65 (  12 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   59 (  30   ~;  25   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :   14 (  14   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f144,plain,
    $false,
    inference(avatar_sat_refutation,[],[f34,f42,f104,f110,f141]) ).

fof(f141,plain,
    ( ~ spl2_3
    | ~ spl2_7 ),
    inference(avatar_contradiction_clause,[],[f140]) ).

fof(f140,plain,
    ( $false
    | ~ spl2_3
    | ~ spl2_7 ),
    inference(trivial_inequality_removal,[],[f134]) ).

fof(f134,plain,
    ( sF0 != sF0
    | ~ spl2_3
    | ~ spl2_7 ),
    inference(superposition,[],[f22,f132]) ).

fof(f132,plain,
    ( sF1 = sF0
    | ~ spl2_3
    | ~ spl2_7 ),
    inference(resolution,[],[f55,f120]) ).

fof(f120,plain,
    ( product(a,sF1,identity)
    | ~ spl2_3
    | ~ spl2_7 ),
    inference(superposition,[],[f41,f80]) ).

fof(f80,plain,
    ( identity = another_identity
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f78]) ).

fof(f78,plain,
    ( spl2_7
  <=> identity = another_identity ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

fof(f41,plain,
    ( product(a,sF1,another_identity)
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f39,plain,
    ( spl2_3
  <=> product(a,sF1,another_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f55,plain,
    ! [X12] :
      ( ~ product(a,X12,identity)
      | sF0 = X12 ),
    inference(resolution,[],[f15,f36]) ).

fof(f36,plain,
    product(a,sF0,identity),
    inference(superposition,[],[f4,f20]) ).

fof(f20,plain,
    inverse(a) = sF0,
    introduced(function_definition,[]) ).

fof(f4,axiom,
    ! [X0] : product(X0,inverse(X0),identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).

fof(f15,axiom,
    ! [X8,X6,X9,X7] :
      ( ~ product(X6,X9,X8)
      | ~ product(X6,X7,X8)
      | X7 = X9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).

fof(f22,plain,
    sF1 != sF0,
    inference(definition_folding,[],[f19,f21,f20]) ).

fof(f21,plain,
    another_inverse(a) = sF1,
    introduced(function_definition,[]) ).

fof(f19,axiom,
    inverse(a) != another_inverse(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).

fof(f110,plain,
    ~ spl2_10,
    inference(avatar_contradiction_clause,[],[f105]) ).

fof(f105,plain,
    ( $false
    | ~ spl2_10 ),
    inference(resolution,[],[f103,f18]) ).

fof(f18,axiom,
    subgroup_member(another_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_identity_in_subgroup) ).

fof(f103,plain,
    ( ! [X0] : ~ subgroup_member(X0)
    | ~ spl2_10 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f102,plain,
    ( spl2_10
  <=> ! [X0] : ~ subgroup_member(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).

fof(f104,plain,
    ( spl2_10
    | spl2_7 ),
    inference(avatar_split_clause,[],[f87,f78,f102]) ).

fof(f87,plain,
    ! [X0] :
      ( identity = another_identity
      | ~ subgroup_member(X0) ),
    inference(resolution,[],[f50,f11]) ).

fof(f11,axiom,
    ! [X6] :
      ( product(X6,another_identity,X6)
      | ~ subgroup_member(X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_identity) ).

fof(f50,plain,
    ! [X2,X3] :
      ( ~ product(X2,X3,X2)
      | identity = X3 ),
    inference(resolution,[],[f15,f2]) ).

fof(f2,axiom,
    ! [X0] : product(X0,identity,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

fof(f42,plain,
    ( spl2_3
    | ~ spl2_1 ),
    inference(avatar_split_clause,[],[f37,f25,f39]) ).

fof(f25,plain,
    ( spl2_1
  <=> subgroup_member(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f37,plain,
    ( ~ subgroup_member(a)
    | product(a,sF1,another_identity) ),
    inference(superposition,[],[f12,f21]) ).

fof(f12,axiom,
    ! [X6] :
      ( product(X6,another_inverse(X6),another_identity)
      | ~ subgroup_member(X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_inverse) ).

fof(f34,plain,
    spl2_1,
    inference(avatar_contradiction_clause,[],[f33]) ).

fof(f33,plain,
    ( $false
    | spl2_1 ),
    inference(resolution,[],[f27,f17]) ).

fof(f17,axiom,
    subgroup_member(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).

fof(f27,plain,
    ( ~ subgroup_member(a)
    | spl2_1 ),
    inference(avatar_component_clause,[],[f25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n014.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   : Mon Aug 29 22:10:18 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  % (21304)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.51  % (21305)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51  % (21308)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51  % (21305)First to succeed.
% 0.21/0.52  % (21318)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.52  % (21303)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.52  % (21303)Refutation not found, incomplete strategy% (21303)------------------------------
% 0.21/0.52  % (21303)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (21303)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (21303)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.52  
% 0.21/0.52  % (21303)Memory used [KB]: 5500
% 0.21/0.52  % (21303)Time elapsed: 0.115 s
% 0.21/0.52  % (21303)Instructions burned: 3 (million)
% 0.21/0.52  % (21303)------------------------------
% 0.21/0.52  % (21303)------------------------------
% 0.21/0.52  % (21304)Also succeeded, but the first one will report.
% 0.21/0.52  % (21309)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.53  % (21331)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.21/0.53  % (21307)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.21/0.53  % (21310)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.53  % (21324)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.53  % (21305)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (21305)------------------------------
% 0.21/0.53  % (21305)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (21305)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (21305)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (21305)Memory used [KB]: 5500
% 0.21/0.53  % (21305)Time elapsed: 0.111 s
% 0.21/0.53  % (21305)Instructions burned: 4 (million)
% 0.21/0.53  % (21305)------------------------------
% 0.21/0.53  % (21305)------------------------------
% 0.21/0.53  % (21301)Success in time 0.17 s
%------------------------------------------------------------------------------