TSTP Solution File: SYN982-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SYN982-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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  : 600s
% DateTime : Thu Jul 21 12:32:28 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   21
% Syntax   : Number of clauses     :   49 (  18 unt;   0 nHn;  49 RR)
%            Number of literals    :  120 (   0 equ;  74 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-1 aty)
%            Number of functors    :   15 (  15 usr;   8 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssNonce(na),
    file('SYN982-1.p',unknown),
    [] ).

cnf(2,axiom,
    ssP(t),
    file('SYN982-1.p',unknown),
    [] ).

cnf(3,axiom,
    ssBf(na),
    file('SYN982-1.p',unknown),
    [] ).

cnf(4,axiom,
    ssP(b),
    file('SYN982-1.p',unknown),
    [] ).

cnf(5,axiom,
    ssP(a),
    file('SYN982-1.p',unknown),
    [] ).

cnf(6,axiom,
    ssNonce(nb(u)),
    file('SYN982-1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ ssIm(pair(u,v))
    | ssIm(v) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ ssIm(pair(u,v))
    | ssIm(u) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(16,axiom,
    ssM(sent(a,b,pair(a,na))),
    file('SYN982-1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ ssIm(triple(u,v,w))
    | ssIm(w) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ ssIm(triple(u,v,w))
    | ssIm(v) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ ssIm(triple(u,v,w))
    | ssIm(u) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ ssM(sent(u,v,w))
    | ssIm(w) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ ssP(u)
    | ~ ssIm(v)
    | ssIk(key(v,u)) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ ssIm(u)
    | ~ ssIm(v)
    | ssIm(pair(v,u)) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ ssP(u)
    | ~ ssP(v)
    | ~ ssIm(w)
    | ssM(sent(v,u,w)) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ ssP(u)
    | ~ ssIm(v)
    | ~ ssIk(key(w,u))
    | ssIm(encr(v,w)) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ ssBf(u)
    | ~ ssM(sent(v,b,pair(v,u)))
    | ssSb(pair(v,u)) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ ssBf(u)
    | ~ ssM(sent(v,b,pair(v,u)))
    | ssM(sent(b,t,triple(b,nb(u),encr(triple(v,u,tb(u)),bt)))) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ ssSb(pair(u,v))
    | ~ ssM(sent(u,b,pair(encr(triple(u,w,tb(v)),bt),encr(nb(v),w))))
    | ssBk(key(w,u)) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ ssBk(key(u,a))
    | ~ ssIk(key(u,b)) ),
    file('SYN982-1.p',unknown),
    [] ).

cnf(73,plain,
    ssIm(pair(a,na)),
    inference(res,[status(thm),theory(equality)],[16,20]),
    [iquote('0:Res:16.0,20.0')] ).

cnf(74,plain,
    ssIm(na),
    inference(res,[status(thm),theory(equality)],[73,14]),
    [iquote('0:Res:73.0,14.0')] ).

cnf(75,plain,
    ssIm(a),
    inference(res,[status(thm),theory(equality)],[73,15]),
    [iquote('0:Res:73.0,15.0')] ).

cnf(82,plain,
    ( ~ ssBf(na)
    | ssSb(pair(a,na)) ),
    inference(res,[status(thm),theory(equality)],[16,30]),
    [iquote('0:Res:16.0,30.1')] ).

cnf(84,plain,
    ssSb(pair(a,na)),
    inference(ssi,[status(thm)],[82,3,1,74]),
    [iquote('0:SSi:82.0,3.0,1.0,74.0')] ).

cnf(86,plain,
    ( ~ ssP(u)
    | ~ ssIm(v)
    | ~ ssP(u)
    | ~ ssIm(w)
    | ssIm(encr(w,v)) ),
    inference(res,[status(thm),theory(equality)],[25,29]),
    [iquote('0:Res:25.2,29.2')] ).

cnf(87,plain,
    ( ~ ssIm(u)
    | ~ ssP(v)
    | ~ ssIm(w)
    | ssIm(encr(w,u)) ),
    inference(obv,[status(thm),theory(equality)],[86]),
    [iquote('0:Obv:86.0')] ).

cnf(88,plain,
    ( ~ ssIm(u)
    | ~ ssIm(v)
    | ssIm(encr(v,u)) ),
    inference(ems,[status(thm)],[87,2]),
    [iquote('0:EmS:87.1,2.0')] ).

cnf(105,plain,
    ( ~ ssBf(na)
    | ssM(sent(b,t,triple(b,nb(na),encr(triple(a,na,tb(na)),bt)))) ),
    inference(res,[status(thm),theory(equality)],[16,33]),
    [iquote('0:Res:16.0,33.1')] ).

cnf(106,plain,
    ( ~ ssP(b)
    | ~ ssP(u)
    | ~ ssIm(pair(u,v))
    | ~ ssBf(v)
    | ssM(sent(b,t,triple(b,nb(v),encr(triple(u,v,tb(v)),bt)))) ),
    inference(res,[status(thm),theory(equality)],[27,33]),
    [iquote('0:Res:27.3,33.1')] ).

cnf(107,plain,
    ssM(sent(b,t,triple(b,nb(na),encr(triple(a,na,tb(na)),bt)))),
    inference(ssi,[status(thm)],[105,3,1,74]),
    [iquote('0:SSi:105.0,3.0,1.0,74.0')] ).

cnf(108,plain,
    ( ~ ssP(u)
    | ~ ssIm(pair(u,v))
    | ~ ssBf(v)
    | ssM(sent(b,t,triple(b,nb(v),encr(triple(u,v,tb(v)),bt)))) ),
    inference(ssi,[status(thm)],[106,4]),
    [iquote('0:SSi:106.0,4.0')] ).

cnf(109,plain,
    ssIm(triple(b,nb(na),encr(triple(a,na,tb(na)),bt))),
    inference(res,[status(thm),theory(equality)],[107,20]),
    [iquote('0:Res:107.0,20.0')] ).

cnf(110,plain,
    ssIm(encr(triple(a,na,tb(na)),bt)),
    inference(res,[status(thm),theory(equality)],[109,17]),
    [iquote('0:Res:109.0,17.0')] ).

cnf(112,plain,
    ssIm(b),
    inference(res,[status(thm),theory(equality)],[109,19]),
    [iquote('0:Res:109.0,19.0')] ).

cnf(113,plain,
    ( ~ ssP(b)
    | ~ ssP(u)
    | ~ ssIm(pair(encr(triple(u,v,tb(w)),bt),encr(nb(w),v)))
    | ~ ssSb(pair(u,w))
    | ssBk(key(v,u)) ),
    inference(res,[status(thm),theory(equality)],[27,34]),
    [iquote('0:Res:27.3,34.1')] ).

cnf(114,plain,
    ( ~ ssP(u)
    | ~ ssIm(pair(encr(triple(u,v,tb(w)),bt),encr(nb(w),v)))
    | ~ ssSb(pair(u,w))
    | ssBk(key(v,u)) ),
    inference(ssi,[status(thm)],[113,4,112]),
    [iquote('0:SSi:113.0,4.0,112.0')] ).

cnf(117,plain,
    ( ~ ssP(u)
    | ~ ssBf(v)
    | ~ ssIm(u)
    | ~ ssIm(v)
    | ssM(sent(b,t,triple(b,nb(v),encr(triple(u,v,tb(v)),bt)))) ),
    inference(sor,[status(thm)],[108,26]),
    [iquote('0:SoR:108.1,26.2')] ).

cnf(125,plain,
    ( ~ ssP(u)
    | ~ ssIm(encr(triple(u,v,tb(w)),bt))
    | ~ ssIm(encr(nb(w),v))
    | ~ ssSb(pair(u,w))
    | ssBk(key(v,u)) ),
    inference(sor,[status(thm)],[114,26]),
    [iquote('0:SoR:114.1,26.2')] ).

cnf(132,plain,
    ( ~ ssP(u)
    | ~ ssBf(v)
    | ~ ssIm(u)
    | ~ ssIm(v)
    | ssIm(triple(b,nb(v),encr(triple(u,v,tb(v)),bt))) ),
    inference(res,[status(thm),theory(equality)],[117,20]),
    [iquote('0:Res:117.4,20.0')] ).

cnf(136,plain,
    ( ~ ssP(u)
    | ~ ssBf(v)
    | ~ ssIm(u)
    | ~ ssIm(v)
    | ssIm(nb(v)) ),
    inference(res,[status(thm),theory(equality)],[132,18]),
    [iquote('0:Res:132.4,18.0')] ).

cnf(138,plain,
    ( ~ ssIm(u)
    | ~ ssBf(u)
    | ssIm(nb(u)) ),
    inference(ems,[status(thm)],[136,4,112]),
    [iquote('0:EmS:136.0,136.2,4.0,112.0')] ).

cnf(144,plain,
    ( ~ ssP(a)
    | ~ ssIm(encr(nb(na),na))
    | ~ ssSb(pair(a,na))
    | ssBk(key(na,a)) ),
    inference(sor,[status(thm)],[125,110]),
    [iquote('0:SoR:125.1,110.0')] ).

cnf(147,plain,
    ( ~ ssSb(pair(a,na))
    | ssBk(key(na,a)) ),
    inference(ssi,[status(thm)],[144,88,6,3,1,74,138,5,75]),
    [iquote('0:SSi:144.1,144.0,88.0,6.0,3.0,1.0,74.0,138.0,3.0,1.0,74.2,3.0,1.0,74.0,5.0,75.2')] ).

cnf(148,plain,
    ssBk(key(na,a)),
    inference(mrr,[status(thm)],[147,84]),
    [iquote('0:MRR:147.0,84.0')] ).

cnf(152,plain,
    ~ ssIk(key(na,b)),
    inference(res,[status(thm),theory(equality)],[148,37]),
    [iquote('0:Res:148.0,37.0')] ).

cnf(158,plain,
    ( ~ ssP(b)
    | ~ ssIm(na) ),
    inference(res,[status(thm),theory(equality)],[25,152]),
    [iquote('0:Res:25.2,152.0')] ).

cnf(159,plain,
    $false,
    inference(ssi,[status(thm)],[158,3,1,74,4,112]),
    [iquote('0:SSi:158.1,158.0,3.0,1.0,74.0,4.0,112.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYN982-1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n003.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue Jul 12 03:55:45 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.43  
% 0.20/0.43  SPASS V 3.9 
% 0.20/0.43  SPASS beiseite: Proof found.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.43  SPASS derived 62 clauses, backtracked 0 clauses, performed 0 splits and kept 81 clauses.
% 0.20/0.43  SPASS allocated 75911 KBytes.
% 0.20/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.43  		0:00:00.04 for the input.
% 0.20/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43  		0:00:00.00 for inferences.
% 0.20/0.43  		0:00:00.00 for the backtracking.
% 0.20/0.43  		0:00:00.01 for the reduction.
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  Here is a proof with depth 6, length 49 :
% 0.20/0.43  % SZS output start Refutation
% See solution above
% 0.20/0.43  Formulae used in the proof : clause1 clause2 clause3 clause4 clause5 clause6 clause14 clause15 clause16 clause17 clause18 clause19 clause20 clause25 clause26 clause27 clause29 clause30 clause33 clause34 clause37
% 0.20/0.43  
%------------------------------------------------------------------------------