%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GRP039-5 : 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_uns --cores 0 -t %d %s

% Computer : n006.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 16:13:48 EDT 2022

% Result   : Unsatisfiable 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   50 (  18 unt;   0 def)
%            Number of atoms       :   93 (  22 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   70 (  27   ~;  40   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   23 (  23   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f260,plain,
    $false,
    inference(avatar_sat_refutation,[],[f38,f44,f46,f257,f259]) ).

fof(f259,plain,
    ( spl0_1
    | spl0_3 ),
    inference(avatar_split_clause,[],[f258,f41,f31]) ).

fof(f31,plain,
    ( spl0_1
  <=> subgroup_member(c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f41,plain,
    ( spl0_3
  <=> subgroup_member(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f258,plain,
    ( subgroup_member(c)
    | spl0_3 ),
    inference(subsumption_resolution,[],[f253,f14]) ).

fof(f14,axiom,
    ~ subgroup_member(d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).

fof(f253,plain,
    ( subgroup_member(c)
    | subgroup_member(d)
    | spl0_3 ),
    inference(subsumption_resolution,[],[f252,f43]) ).

fof(f43,plain,
    ( ~ subgroup_member(a)
    | spl0_3 ),
    inference(avatar_component_clause,[],[f41]) ).

fof(f252,plain,
    ( subgroup_member(a)
    | subgroup_member(c)
    | subgroup_member(d)
    | spl0_3 ),
    inference(superposition,[],[f9,f248]) ).

fof(f248,plain,
    ( c = element_in_O2(a,d)
    | spl0_3 ),
    inference(forward_demodulation,[],[f247,f126]) ).

fof(f126,plain,
    c = multiply(inverse(b),multiply(c,d)),
    inference(forward_demodulation,[],[f116,f115]) ).

fof(f115,plain,
    ! [X9] : multiply(inverse(a),X9) = multiply(inverse(b),multiply(c,X9)),
    inference(superposition,[],[f59,f52]) ).

fof(f52,plain,
    ! [X12] : multiply(c,X12) = multiply(b,multiply(inverse(a),X12)),
    inference(superposition,[],[f3,f12]) ).

fof(f12,axiom,
    multiply(b,inverse(a)) = c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).

fof(f3,axiom,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).

fof(f59,plain,
    ! [X10,X11] : multiply(inverse(X10),multiply(X10,X11)) = X11,
    inference(forward_demodulation,[],[f51,f1]) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

fof(f51,plain,
    ! [X10,X11] : multiply(inverse(X10),multiply(X10,X11)) = multiply(identity,X11),
    inference(superposition,[],[f3,f2]) ).

fof(f2,axiom,
    ! [X0] : identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

fof(f116,plain,
    c = multiply(inverse(a),d),
    inference(superposition,[],[f59,f13]) ).

fof(f13,axiom,
    multiply(a,c) = d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).

fof(f247,plain,
    ( element_in_O2(a,d) = multiply(inverse(b),multiply(c,d))
    | spl0_3 ),
    inference(forward_demodulation,[],[f244,f115]) ).

fof(f244,plain,
    ( element_in_O2(a,d) = multiply(inverse(a),d)
    | spl0_3 ),
    inference(superposition,[],[f59,f88]) ).

fof(f88,plain,
    ( d = multiply(a,element_in_O2(a,d))
    | spl0_3 ),
    inference(resolution,[],[f76,f43]) ).

fof(f76,plain,
    ! [X3] :
      ( subgroup_member(X3)
      | d = multiply(X3,element_in_O2(X3,d)) ),
    inference(resolution,[],[f10,f14]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( subgroup_member(X1)
      | subgroup_member(X0)
      | multiply(X0,element_in_O2(X0,X1)) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( subgroup_member(element_in_O2(X0,X1))
      | subgroup_member(X0)
      | subgroup_member(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).

fof(f257,plain,
    ( ~ spl0_1
    | spl0_3 ),
    inference(avatar_split_clause,[],[f237,f41,f31]) ).

fof(f237,plain,
    ( ~ subgroup_member(c)
    | spl0_3 ),
    inference(resolution,[],[f157,f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( subgroup_member(inverse(X0))
      | ~ subgroup_member(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_inverse) ).

fof(f157,plain,
    ( ~ subgroup_member(inverse(c))
    | spl0_3 ),
    inference(subsumption_resolution,[],[f156,f43]) ).

fof(f156,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(inverse(c)) ),
    inference(subsumption_resolution,[],[f154,f11]) ).

fof(f11,axiom,
    subgroup_member(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).

fof(f154,plain,
    ( ~ subgroup_member(b)
    | subgroup_member(a)
    | ~ subgroup_member(inverse(c)) ),
    inference(superposition,[],[f15,f128]) ).

fof(f128,plain,
    a = multiply(inverse(c),b),
    inference(superposition,[],[f59,f97]) ).

fof(f97,plain,
    b = multiply(c,a),
    inference(forward_demodulation,[],[f92,f6]) ).

fof(f6,axiom,
    ! [X0] : multiply(X0,identity) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

fof(f92,plain,
    multiply(c,a) = multiply(b,identity),
    inference(superposition,[],[f52,f2]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( subgroup_member(multiply(X0,X1))
      | ~ subgroup_member(X0)
      | ~ subgroup_member(X1) ),
    inference(equality_resolution,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X0,X1] :
      ( subgroup_member(X2)
      | ~ subgroup_member(X1)
      | ~ subgroup_member(X0)
      | multiply(X0,X1) != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiply) ).

fof(f46,plain,
    ( ~ spl0_3
    | spl0_2 ),
    inference(avatar_split_clause,[],[f45,f35,f41]) ).

fof(f35,plain,
    ( spl0_2
  <=> subgroup_member(inverse(a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f45,plain,
    ( ~ subgroup_member(a)
    | spl0_2 ),
    inference(resolution,[],[f37,f4]) ).

fof(f37,plain,
    ( ~ subgroup_member(inverse(a))
    | spl0_2 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f44,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f39,f41,f31]) ).

fof(f39,plain,
    ( ~ subgroup_member(a)
    | ~ subgroup_member(c) ),
    inference(subsumption_resolution,[],[f28,f14]) ).

fof(f28,plain,
    ( ~ subgroup_member(c)
    | ~ subgroup_member(a)
    | subgroup_member(d) ),
    inference(superposition,[],[f15,f13]) ).

fof(f38,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f29,f35,f31]) ).

fof(f29,plain,
    ( ~ subgroup_member(inverse(a))
    | subgroup_member(c) ),
    inference(subsumption_resolution,[],[f27,f11]) ).

fof(f27,plain,
    ( ~ subgroup_member(b)
    | ~ subgroup_member(inverse(a))
    | subgroup_member(c) ),
    inference(superposition,[],[f15,f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : GRP039-5 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33  % Computer : n006.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon Aug 29 22:08:40 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.48  % (5324)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.49  % (5330)dis+4_1:1_bd=off:cond=fast:fde=unused:lcm=reverse:lma=on:nicw=on:nwc=2.0:s2a=on:s2agt=16:sac=on:sp=frequency:i=23:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/23Mi)
% 0.19/0.49  % (5321)lrs+10_1:1_bd=off:drc=off:lcm=reverse:nwc=5.0:sd=1:sgt=16:spb=goal_then_units:ss=axioms:to=lpo:i=43:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/43Mi)
% 0.19/0.49  % (5321)First to succeed.
% 0.19/0.49  % (5341)lrs+1010_1:1_bd=off:fsr=off:sd=1:sos=on:ss=axioms:i=67:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/67Mi)
% 0.19/0.49  % (5337)lrs+1003_1:1024_add=large:afr=on:cond=fast:fsr=off:gs=on:sos=on:sp=reverse_arity:i=28:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/28Mi)
% 0.19/0.49  % (5333)dis+1011_3:29_av=off:awrs=decay:awrsf=32:bce=on:drc=off:fde=unused:gsp=on:irw=on:nwc=2.0:spb=goal_then_units:updr=off:urr=ec_only:i=29:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/29Mi)
% 0.19/0.50  % (5323)dis+1011_1:16_fsr=off:nwc=2.0:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.50  % (5339)lrs+1011_1:1_afp=100000:afr=on:amm=sco:bd=preordered:cond=fast:newcnf=on:nm=4:sos=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (5322)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.19/0.50  % (5320)lrs+10_1:16_awrs=converge:awrsf=40:br=off:ep=RSTC:flr=on:gsp=on:nwc=3.0:sos=on:urr=on:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.51  % (5331)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=5:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.19/0.51  % (5320)Instruction limit reached!
% 0.19/0.51  % (5320)------------------------------
% 0.19/0.51  % (5320)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (5320)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (5320)Termination reason: Unknown
% 0.19/0.51  % (5320)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (5320)Memory used [KB]: 5884
% 0.19/0.51  % (5320)Time elapsed: 0.125 s
% 0.19/0.51  % (5320)Instructions burned: 4 (million)
% 0.19/0.51  % (5320)------------------------------
% 0.19/0.51  % (5320)------------------------------
% 0.19/0.51  % (5318)lrs+10_1:1_kws=precedence:lwlo=on:tgt=ground:i=99966:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99966Mi)
% 0.19/0.51  % (5343)lrs+1011_1:1_aac=none:bsr=unit_only:ep=R:sac=on:sos=all:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.51  % (5319)dis+21_1:1_av=off:fd=off:lcm=predicate:sos=on:spb=goal:urr=ec_only:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/42Mi)
% 0.19/0.51  % (5347)lrs+10_1:1_av=off:sd=2:sos=on:sp=reverse_arity:ss=axioms:to=lpo:i=73:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/73Mi)
% 0.19/0.51  % (5336)ott+2_1:64_afp=40000:bd=off:irw=on:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.52  % (5321)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (5321)------------------------------
% 0.19/0.52  % (5321)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (5321)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (5321)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (5321)Memory used [KB]: 6012
% 0.19/0.52  % (5321)Time elapsed: 0.113 s
% 0.19/0.52  % (5321)Instructions burned: 8 (million)
% 0.19/0.52  % (5321)------------------------------
% 0.19/0.52  % (5321)------------------------------
% 0.19/0.52  % (5314)Success in time 0.18 s
%------------------------------------------------------------------------------