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