↑ Up

Vampire---5.0.1.THM-Ref.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : GRP711+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 10:16:01 AM UTC 2026

% Result   : Theorem 2.21s 1.24s
% Output   : Refutation 2.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   77 (  29 unt;   3 def)
%            Number of atoms       :  135 (  77 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  107 (  49   ~;  45   |;   6   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   74 (   0 sgn  71   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] : mult(X0,unit) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).

fof(f2,axiom,
    ! [X0] : mult(unit,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).

fof(f3,axiom,
    ! [X0,X1,X2] : mult(X2,mult(X1,mult(X1,X0))) = mult(mult(mult(X2,X1),X1),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).

fof(f4,axiom,
    ! [X0] : mult(X0,i(X0)) = unit,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).

fof(f5,axiom,
    ! [X0] : mult(i(X0),X0) = unit,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

fof(f6,conjecture,
    ! [X0,X1,X2] :
      ( ( mult(X0,X1) = mult(X0,X2)
       => X1 = X2 )
      & ( mult(X1,X0) = mult(X2,X0)
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f7,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( mult(X0,X1) = mult(X0,X2)
         => X1 = X2 )
        & ( mult(X1,X0) = mult(X2,X0)
         => X1 = X2 ) ),
    inference(negated_conjecture,[status(cth)],[f6]) ).

fof(f8,plain,
    ? [X0,X1,X2] :
      ( ( X1 != X2
        & mult(X0,X1) = mult(X0,X2) )
      | ( X1 != X2
        & mult(X1,X0) = mult(X2,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f9,plain,
    ( ( sK1 != sK2
      & mult(sK0,sK1) = mult(sK0,sK2) )
    | ( sK1 != sK2
      & mult(sK1,sK0) = mult(sK2,sK0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).

fof(f10,plain,
    ! [X0] : mult(X0,unit) = X0,
    inference(cnf_transformation,[],[f1]) ).

fof(f11,plain,
    ! [X0] : mult(unit,X0) = X0,
    inference(cnf_transformation,[],[f2]) ).

fof(f12,plain,
    ! [X2,X0,X1] : mult(X2,mult(X1,mult(X1,X0))) = mult(mult(mult(X2,X1),X1),X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f13,plain,
    ! [X0] : unit = mult(X0,i(X0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f14,plain,
    ! [X0] : unit = mult(i(X0),X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f15,plain,
    ( mult(sK0,sK1) = mult(sK0,sK2)
    | mult(sK1,sK0) = mult(sK2,sK0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f18,plain,
    ( sK1 != sK2
    | sK1 != sK2 ),
    inference(cnf_transformation,[],[f9]) ).

fof(f19,plain,
    sK1 != sK2,
    inference(duplicate_literal_removal,[],[f18]) ).

fof(f21,definition,
    ( spl3_1
  <=> mult(sK1,sK0) = mult(sK2,sK0) ),
    introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).

fof(f23,plain,
    ( mult(sK1,sK0) = mult(sK2,sK0)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f21]) ).

fof(f25,definition,
    ( spl3_2
  <=> mult(sK0,sK1) = mult(sK0,sK2) ),
    introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).

fof(f27,plain,
    ( mult(sK0,sK1) = mult(sK0,sK2)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f25]) ).

fof(f28,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f15,f25,f21]) ).

fof(f30,definition,
    ( spl3_3
  <=> sK1 = sK2 ),
    introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).

fof(f32,plain,
    ( sK1 != sK2
    | spl3_3 ),
    inference(avatar_component_clause,[],[f30]) ).

fof(f35,plain,
    ~ spl3_3,
    inference(avatar_split_clause,[],[f19,f30]) ).

fof(f43,plain,
    ! [X0,X1] : mult(X0,mult(i(X0),mult(i(X0),X1))) = mult(mult(unit,i(X0)),X1),
    inference(superposition,[],[f12,f13]) ).

fof(f44,plain,
    ! [X0,X1] : mult(unit,mult(X0,mult(X0,X1))) = mult(mult(X0,X0),X1),
    inference(superposition,[],[f12,f11]) ).

fof(f45,plain,
    ! [X2,X3,X0,X1] : mult(mult(mult(X0,X1),X1),mult(X2,mult(X2,X3))) = mult(mult(mult(X0,mult(X1,mult(X1,X2))),X2),X3),
    inference(superposition,[],[f12,f12]) ).

fof(f46,plain,
    ! [X0,X1] : mult(i(X0),mult(X0,mult(X0,X1))) = mult(mult(unit,X0),X1),
    inference(superposition,[],[f12,f14]) ).

fof(f47,plain,
    ( ! [X0] : mult(sK0,mult(sK2,mult(sK2,X0))) = mult(mult(mult(sK0,sK1),sK2),X0)
    | ~ spl3_2 ),
    inference(superposition,[],[f12,f27]) ).

fof(f51,plain,
    ! [X0,X1] : unit = mult(X0,mult(X1,mult(X1,i(mult(mult(X0,X1),X1))))),
    inference(superposition,[],[f12,f13]) ).

fof(f52,plain,
    ! [X0,X1] : mult(mult(X0,X1),X1) = mult(X0,mult(X1,mult(X1,unit))),
    inference(superposition,[],[f10,f12]) ).

fof(f54,plain,
    ! [X0,X1] : mult(mult(X0,X1),X1) = mult(X0,mult(X1,X1)),
    inference(forward_demodulation,[],[f52,f10]) ).

fof(f57,plain,
    ! [X0,X1] : mult(X0,X1) = mult(i(X0),mult(X0,mult(X0,X1))),
    inference(forward_demodulation,[],[f46,f11]) ).

fof(f58,plain,
    ! [X2,X3,X0,X1] : mult(mult(mult(X0,mult(X1,mult(X1,X2))),X2),X3) = mult(X0,mult(X1,mult(X1,mult(X2,mult(X2,X3))))),
    inference(forward_demodulation,[],[f45,f12]) ).

fof(f59,plain,
    ! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
    inference(forward_demodulation,[],[f44,f11]) ).

fof(f60,plain,
    ! [X0,X1] : mult(i(X0),X1) = mult(X0,mult(i(X0),mult(i(X0),X1))),
    inference(forward_demodulation,[],[f43,f11]) ).

fof(f67,plain,
    ( mult(mult(sK0,sK1),sK2) = mult(sK0,mult(sK2,mult(sK2,unit)))
    | ~ spl3_2 ),
    inference(superposition,[],[f10,f47]) ).

fof(f71,plain,
    ( mult(mult(sK0,sK1),sK2) = mult(sK0,mult(sK2,sK2))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f67,f10]) ).

fof(f73,plain,
    ( ! [X0] : mult(sK0,mult(sK2,mult(sK2,X0))) = mult(mult(sK0,mult(sK2,sK2)),X0)
    | ~ spl3_2 ),
    inference(superposition,[],[f47,f71]) ).

fof(f135,plain,
    ( ! [X0] : mult(mult(mult(sK0,sK1),sK2),X0) = mult(i(mult(mult(sK0,sK1),sK2)),mult(sK0,mult(sK2,mult(sK2,mult(mult(mult(sK0,sK1),sK2),X0)))))
    | ~ spl3_2 ),
    inference(superposition,[],[f57,f47]) ).

fof(f140,plain,
    ( ! [X0] : mult(sK0,mult(sK2,mult(sK2,X0))) = mult(i(mult(mult(sK0,sK1),sK2)),mult(sK0,mult(sK2,mult(sK2,mult(sK0,mult(sK2,mult(sK2,X0)))))))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f135,f47]) ).

fof(f151,plain,
    ( ! [X0] : mult(sK0,mult(sK2,mult(sK2,X0))) = mult(i(mult(sK0,mult(sK2,sK2))),mult(sK0,mult(sK2,mult(sK2,mult(sK0,mult(sK2,mult(sK2,X0)))))))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f140,f71]) ).

fof(f163,plain,
    ! [X0,X1] : unit = mult(X0,mult(X1,mult(X1,i(mult(X0,mult(X1,X1)))))),
    inference(forward_demodulation,[],[f51,f54]) ).

fof(f1194,plain,
    ( mult(sK0,unit) = mult(i(mult(sK0,mult(sK2,sK2))),mult(sK0,mult(sK2,mult(sK2,mult(sK0,unit)))))
    | ~ spl3_2 ),
    inference(superposition,[],[f151,f163]) ).

fof(f1208,plain,
    ( sK0 = mult(i(mult(sK0,mult(sK2,sK2))),mult(sK0,mult(sK2,mult(sK2,sK0))))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1194,f10]) ).

fof(f1213,plain,
    ( sK0 = mult(mult(sK0,mult(sK2,sK2)),mult(i(mult(sK0,mult(sK2,sK2))),sK0))
    | ~ spl3_2 ),
    inference(superposition,[],[f60,f1208]) ).

fof(f1218,plain,
    ( sK0 = mult(sK0,mult(sK2,mult(sK2,mult(i(mult(sK0,mult(sK2,sK2))),sK0))))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1213,f73]) ).

fof(f1223,plain,
    ( sK0 = mult(i(sK0),mult(sK0,sK0))
    | ~ spl3_2 ),
    inference(superposition,[],[f57,f1218]) ).

fof(f1259,plain,
    ( ! [X0,X1] : mult(X0,mult(i(sK0),mult(i(sK0),mult(mult(sK0,sK0),mult(mult(sK0,sK0),X1))))) = mult(mult(mult(X0,mult(i(sK0),sK0)),mult(sK0,sK0)),X1)
    | ~ spl3_2 ),
    inference(superposition,[],[f58,f1223]) ).

fof(f1266,plain,
    ( ! [X0,X1] : mult(X0,mult(i(sK0),mult(i(sK0),mult(mult(sK0,sK0),mult(mult(sK0,sK0),X1))))) = mult(mult(mult(X0,unit),mult(sK0,sK0)),X1)
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1259,f14]) ).

fof(f1271,plain,
    ( ! [X0,X1] : mult(X0,mult(i(sK0),mult(i(sK0),mult(mult(sK0,sK0),mult(mult(sK0,sK0),X1))))) = mult(mult(X0,mult(sK0,sK0)),X1)
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1266,f10]) ).

fof(f1273,plain,
    ( ! [X0,X1] : mult(mult(X0,mult(sK0,sK0)),X1) = mult(X0,mult(i(sK0),mult(i(sK0),mult(sK0,mult(sK0,mult(mult(sK0,sK0),X1))))))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1271,f59]) ).

fof(f1274,plain,
    ( ! [X0,X1] : mult(mult(X0,mult(sK0,sK0)),X1) = mult(X0,mult(i(sK0),mult(sK0,mult(mult(sK0,sK0),X1))))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1273,f57]) ).

fof(f1275,plain,
    ( ! [X0,X1] : mult(mult(X0,mult(sK0,sK0)),X1) = mult(X0,mult(i(sK0),mult(sK0,mult(sK0,mult(sK0,X1)))))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1274,f59]) ).

fof(f1276,plain,
    ( ! [X0,X1] : mult(mult(X0,mult(sK0,sK0)),X1) = mult(X0,mult(sK0,mult(sK0,X1)))
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1275,f57]) ).

fof(f1482,plain,
    ( ! [X0] : mult(unit,X0) = mult(i(mult(sK0,sK0)),mult(sK0,mult(sK0,X0)))
    | ~ spl3_2 ),
    inference(superposition,[],[f1276,f14]) ).

fof(f1558,plain,
    ( ! [X0] : mult(i(mult(sK0,sK0)),mult(sK0,mult(sK0,X0))) = X0
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1482,f11]) ).

fof(f1601,plain,
    ( sK2 = mult(i(mult(sK0,sK0)),mult(sK0,mult(sK0,sK1)))
    | ~ spl3_2 ),
    inference(superposition,[],[f1558,f27]) ).

fof(f1640,plain,
    ( sK1 = sK2
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f1601,f1558]) ).

fof(f1641,plain,
    ( $false
    | ~ spl3_2
    | spl3_3 ),
    inference(forward_subsumption_resolution,[],[f1640,f32]) ).

fof(f1642,plain,
    ( ~ spl3_2
    | spl3_3 ),
    inference(avatar_contradiction_clause,[],[f1641]) ).

fof(f1646,plain,
    ( ! [X0] : mult(sK2,mult(sK0,mult(sK0,X0))) = mult(mult(mult(sK1,sK0),sK0),X0)
    | ~ spl3_1 ),
    inference(superposition,[],[f12,f23]) ).

fof(f1647,plain,
    ( ! [X0] : mult(sK2,mult(sK0,mult(sK0,X0))) = mult(sK1,mult(sK0,mult(sK0,X0)))
    | ~ spl3_1 ),
    inference(forward_demodulation,[],[f1646,f12]) ).

fof(f1653,plain,
    ( mult(sK2,unit) = mult(sK1,unit)
    | ~ spl3_1 ),
    inference(superposition,[],[f1647,f163]) ).

fof(f1666,plain,
    ( sK1 = mult(sK2,unit)
    | ~ spl3_1 ),
    inference(forward_demodulation,[],[f1653,f10]) ).

fof(f1669,plain,
    ( sK1 = sK2
    | ~ spl3_1 ),
    inference(forward_demodulation,[],[f1666,f10]) ).

fof(f1670,plain,
    ( $false
    | ~ spl3_1
    | spl3_3 ),
    inference(forward_subsumption_resolution,[],[f1669,f32]) ).

fof(f1671,plain,
    ( ~ spl3_1
    | spl3_3 ),
    inference(avatar_contradiction_clause,[],[f1670]) ).

cnf(s1,plain,
    ( spl3_1
    | spl3_2 ),
    inference(sat_conversion,[],[f28]) ).

cnf(s4,plain,
    ~ spl3_3,
    inference(sat_conversion,[],[f35]) ).

cnf(s5,plain,
    ( ~ spl3_2
    | spl3_3 ),
    inference(sat_conversion,[],[f1642]) ).

cnf(s6,plain,
    ( ~ spl3_1
    | spl3_3 ),
    inference(sat_conversion,[],[f1671]) ).

cnf(s7,plain,
    ~ spl3_1,
    inference(rat,[],[s6,s4]) ).

cnf(s8,plain,
    ~ spl3_2,
    inference(rat,[],[s5,s4]) ).

cnf(s9,plain,
    $false,
    inference(rat,[],[s1,s8,s7]) ).

fof(f1672,plain,
    $false,
    inference(avatar_sat_refutation,[],[s9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : GRP711+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43  % Computer : n013.cluster.edu
% 0.18/0.43  % Model    : x86_64 x86_64
% 0.18/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43  % Memory   : 8046.5625MB
% 0.18/0.43  % OS       : Linux 6.8.0-71-generic
% 0.18/0.43  % CPULimit : 300
% 0.18/0.43  % WCLimit  : 300
% 0.18/0.43  % DateTime : Sun Sep 27 10:36:22 UTC 2026
% 0.18/0.44  % CPUTime  : 
% 0.18/0.44  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.21/1.24  % (28782)Detected formulas, will run a generic FOF schedule.
% 2.21/1.24  % (28872)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2274385690:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.21/1.24  % (28872)First to succeed.
% 2.21/1.24  % (28872)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28782"
% 2.21/1.24  % (28869)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3084471176:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.21/1.24  % (28865)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2145391045:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.21/1.24  % (28864)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1574811462:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.21/1.24  % (28867)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=804494226:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.21/1.24  % (28873)dis-21_1_sil=8000:lcm=predicate:random_seed=2061939247:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.21/1.24  % (28871)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1024475234:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.21/1.24  % (28873)Refutation not found, incomplete strategy
% 2.21/1.24  % (28873)------------------------------
% 2.21/1.24  % (28873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/1.24  % (28873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/1.24  % (28873)CaDiCaL version: 2.1.3
% 2.21/1.24  % (28873)Termination reason: Refutation not found, incomplete strategy
% 2.21/1.24  % (28873)Time elapsed: 0.001 s
% 2.21/1.24  % (28873)Peak memory usage: 88 MB
% 2.21/1.24  % (28869)Instruction limit reached! 
% 2.21/1.24  % (28869)------------------------------
% 2.21/1.24  % (28869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/1.24  % (28869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/1.24  % (28869)CaDiCaL version: 2.1.3
% 2.21/1.24  % (28869)Termination reason: Instruction limit
% 2.21/1.24  % (28869)Termination phase: Saturation
% 2.21/1.24  % (28869)Time elapsed: 0.053 s
% 2.21/1.24  % (28869)Peak memory usage: 89 MB
% 2.21/1.24  % (28869)Instructions burned: 109 (million)
% 2.21/1.24  % (28871)Instruction limit reached! 
% 2.21/1.24  % (28871)------------------------------
% 2.21/1.24  % (28871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/1.24  % (28871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/1.24  % (28871)CaDiCaL version: 2.1.3
% 2.21/1.24  % (28871)Termination reason: Instruction limit
% 2.21/1.24  % (28871)Termination phase: Saturation
% 2.21/1.24  % (28871)Time elapsed: 0.061 s
% 2.21/1.24  % (28871)Peak memory usage: 88 MB
% 2.21/1.24  % (28871)Instructions burned: 122 (million)
% 2.21/1.24  % (28872)Refutation found. Thanks to Tanya!
% 2.21/1.24  % SZS status Theorem for theBenchmark
% 2.21/1.24  % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.43  % (28872)------------------------------
% 2.80/1.43  % (28872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.43  % (28872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.43  % (28872)CaDiCaL version: 2.1.3
% 2.80/1.43  % (28872)Termination reason: Refutation
% 2.80/1.43  % (28872)Time elapsed: 0.030 s
% 2.80/1.43  % (28872)Peak memory usage: 90 MB
% 2.80/1.43  % (28872)Instructions burned: 102 (million)
% 2.80/1.43  % (28872)------------------------------
% 2.80/1.43  % (28872)------------------------------
% 2.80/1.43  % (28782)Success in time 0.289 s
% 2.80/1.43  % Vampire exiting
%------------------------------------------------------------------------------