TSTP Solution File: SWV770-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV770-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 : Wed Jul 20 21:45:05 EDT 2022
% Result : Unsatisfiable 115.83s 116.10s
% Output : Refutation 115.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 44 ( 26 unt; 8 nHn; 44 RR)
% Number of literals : 66 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
~ hBOOL(c_in(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v)),
file('SWV770-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ hBOOL(c_in(u,c_Set_Oinsert(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),w),w))
| equal(u,v) ),
file('SWV770-1.p',unknown),
[] ).
cnf(29,axiom,
~ equal(c_Set_Oinsert(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),
file('SWV770-1.p',unknown),
[] ).
cnf(51,axiom,
equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_List_Oset(c_List_Olist_ONil(u),u)),
file('SWV770-1.p',unknown),
[] ).
cnf(87,axiom,
equal(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),c_Set_Oinsert(v,c_Set_Oinsert(u,w,x),x)),
file('SWV770-1.p',unknown),
[] ).
cnf(107,axiom,
( ~ hBOOL(hAPP(u,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(u,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(u,v)) ),
file('SWV770-1.p',unknown),
[] ).
cnf(126,axiom,
equal(c_Set_Oinsert(u,c_Set_Oinsert(u,v,w),w),c_Set_Oinsert(u,v,w)),
file('SWV770-1.p',unknown),
[] ).
cnf(127,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,v,w),x))
| hBOOL(hAPP(v,x))
| equal(u,x) ),
file('SWV770-1.p',unknown),
[] ).
cnf(170,axiom,
c_List_Odistinct(c_List_Olist_ONil(u),u),
file('SWV770-1.p',unknown),
[] ).
cnf(181,axiom,
hBOOL(hAPP(c_Set_Oinsert(u,v,w),u)),
file('SWV770-1.p',unknown),
[] ).
cnf(254,axiom,
hBOOL(c_in(u,c_Set_Oinsert(u,v,w),w)),
file('SWV770-1.p',unknown),
[] ).
cnf(338,axiom,
equal(c_Set_Oinsert(u,c_List_Oset(v,w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
file('SWV770-1.p',unknown),
[] ).
cnf(452,axiom,
( ~ hBOOL(c_in(u,c_List_Oset(v,w),w))
| ~ c_List_Odistinct(c_List_Olist_OCons(u,v,w),w) ),
file('SWV770-1.p',unknown),
[] ).
cnf(454,axiom,
( ~ c_List_Odistinct(u,v)
| hBOOL(c_in(w,c_List_Oset(u,v),v))
| c_List_Odistinct(c_List_Olist_OCons(w,u,v),v) ),
file('SWV770-1.p',unknown),
[] ).
cnf(482,axiom,
( ~ hBOOL(c_in(u,c_List_Oset(c_List_Olist_OCons(v,w,x),x),x))
| hBOOL(c_in(u,c_List_Oset(w,x),x))
| equal(u,v) ),
file('SWV770-1.p',unknown),
[] ).
cnf(526,axiom,
~ equal(c_List_Olist_OCons(u,v,w),v),
file('SWV770-1.p',unknown),
[] ).
cnf(642,axiom,
( ~ hBOOL(hAPP(u,v))
| hBOOL(c_in(v,u,w)) ),
file('SWV770-1.p',unknown),
[] ).
cnf(689,axiom,
~ hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(u,c_Message_Omsg_OMPair(v,hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
file('SWV770-1.p',unknown),
[] ).
cnf(883,plain,
( ~ hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(u,c_Message_Omsg_OMPair(v,hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(c_List_Olist_OCons(w,v_evs,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent))
| equal(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(u,c_Message_Omsg_OMPair(v,hAPP(c_Message_Omsg_OKey,v_K)))),w) ),
inference(res,[status(thm),theory(equality)],[482,689]),
[iquote('0:Res:482.1,689.0')] ).
cnf(1149,plain,
~ hBOOL(c_in(u,c_List_Oset(c_List_Olist_ONil(v),v),v)),
inference(spl,[status(thm),theory(equality)],[51,10]),
[iquote('0:SpL:51.0,10.0')] ).
cnf(3140,plain,
hBOOL(c_in(u,c_List_Oset(c_List_Olist_OCons(u,v,w),w),w)),
inference(spr,[status(thm),theory(equality)],[338,254]),
[iquote('0:SpR:338.0,254.0')] ).
cnf(3141,plain,
equal(c_Set_Oinsert(u,c_List_Oset(c_List_Olist_OCons(u,v,w),w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
inference(spr,[status(thm),theory(equality)],[338,126]),
[iquote('0:SpR:338.0,126.0')] ).
cnf(3219,plain,
equal(c_List_Oset(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
inference(rew,[status(thm),theory(equality)],[338,3141]),
[iquote('0:Rew:338.0,3141.0')] ).
cnf(3742,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),w)) ),
inference(res,[status(thm),theory(equality)],[181,107]),
[iquote('0:Res:181.0,107.0')] ).
cnf(5535,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),w))
| equal(w,u) ),
inference(res,[status(thm),theory(equality)],[642,24]),
[iquote('0:Res:642.1,24.0')] ).
cnf(5676,plain,
~ c_List_Odistinct(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),w),
inference(res,[status(thm),theory(equality)],[3140,452]),
[iquote('0:Res:3140.0,452.0')] ).
cnf(6853,plain,
hBOOL(hAPP(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),v)),
inference(spr,[status(thm),theory(equality)],[87,181]),
[iquote('0:SpR:87.0,181.0')] ).
cnf(11084,plain,
( ~ c_List_Odistinct(c_List_Olist_ONil(u),u)
| c_List_Odistinct(c_List_Olist_OCons(v,c_List_Olist_ONil(u),u),u) ),
inference(res,[status(thm),theory(equality)],[454,1149]),
[iquote('0:Res:454.1,1149.0')] ).
cnf(11091,plain,
c_List_Odistinct(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),v),
inference(mrr,[status(thm)],[11084,170]),
[iquote('0:MRR:11084.0,170.0')] ).
cnf(71021,plain,
hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,u,v),v),w)),
inference(res,[status(thm),theory(equality)],[6853,3742]),
[iquote('0:Res:6853.0,3742.0')] ).
cnf(71022,plain,
hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),v),w)),
inference(rew,[status(thm),theory(equality)],[87,71021]),
[iquote('0:Rew:87.0,71021.0')] ).
cnf(71058,plain,
( hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),w))
| equal(c_Public_Okeymode_OEncryption,w) ),
inference(res,[status(thm),theory(equality)],[71022,127]),
[iquote('0:Res:71022.0,127.0')] ).
cnf(71250,plain,
( equal(c_Public_Okeymode_OEncryption,u)
| equal(u,c_Public_Okeymode_OSignature) ),
inference(res,[status(thm),theory(equality)],[71058,5535]),
[iquote('0:Res:71058.0,5535.0')] ).
cnf(75428,plain,
( equal(c_List_Olist_ONil(u),c_Public_Okeymode_OEncryption)
| c_List_Odistinct(c_Public_Okeymode_OSignature,u) ),
inference(spr,[status(thm),theory(equality)],[71250,170]),
[iquote('0:SpR:71250.1,170.0')] ).
cnf(79033,plain,
( equal(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),c_Public_Okeymode_OEncryption)
| c_List_Odistinct(c_Public_Okeymode_OSignature,v) ),
inference(spr,[status(thm),theory(equality)],[71250,11091]),
[iquote('0:SpR:71250.1,11091.0')] ).
cnf(81824,plain,
( ~ c_List_Odistinct(c_Public_Okeymode_OSignature,u)
| equal(c_List_Olist_OCons(v,c_List_Olist_OCons(v,w,u),u),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[71250,5676]),
[iquote('0:SpL:71250.1,5676.0')] ).
cnf(82086,plain,
( equal(c_List_Olist_OCons(u,c_Public_Okeymode_OEncryption,v),c_Public_Okeymode_OEncryption)
| c_List_Odistinct(c_Public_Okeymode_OSignature,v) ),
inference(rew,[status(thm),theory(equality)],[75428,79033]),
[iquote('0:Rew:75428.0,79033.0')] ).
cnf(82087,plain,
c_List_Odistinct(c_Public_Okeymode_OSignature,u),
inference(mrr,[status(thm)],[82086,526]),
[iquote('0:MRR:82086.0,526.0')] ).
cnf(82882,plain,
equal(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[81824,82087]),
[iquote('0:MRR:81824.0,82087.0')] ).
cnf(82886,plain,
equal(c_List_Oset(c_List_Olist_OCons(u,v,w),w),c_List_Oset(c_Public_Okeymode_OEncryption,w)),
inference(rew,[status(thm),theory(equality)],[82882,3219]),
[iquote('0:Rew:82882.0,3219.0')] ).
cnf(82958,plain,
hBOOL(c_in(u,c_List_Oset(c_Public_Okeymode_OEncryption,v),v)),
inference(rew,[status(thm),theory(equality)],[82886,3140]),
[iquote('0:Rew:82886.0,3140.0')] ).
cnf(83213,plain,
( ~ hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(u,c_Message_Omsg_OMPair(v,hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(c_Public_Okeymode_OEncryption,tc_Event_Oevent),tc_Event_Oevent))
| equal(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(u,c_Message_Omsg_OMPair(v,hAPP(c_Message_Omsg_OKey,v_K)))),w) ),
inference(rew,[status(thm),theory(equality)],[82886,883]),
[iquote('0:Rew:82886.0,883.0')] ).
cnf(106699,plain,
~ hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(u,c_Message_Omsg_OMPair(v,hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(c_Public_Okeymode_OEncryption,tc_Event_Oevent),tc_Event_Oevent)),
inference(aed,[status(thm),theory(equality)],[29,83213]),
[iquote('0:AED:29.0,83213.1')] ).
cnf(106700,plain,
$false,
inference(mrr,[status(thm)],[106699,82958]),
[iquote('0:MRR:106699.0,82958.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV770-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 12:18:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 115.83/116.10
% 115.83/116.10 SPASS V 3.9
% 115.83/116.10 SPASS beiseite: Proof found.
% 115.83/116.10 % SZS status Theorem
% 115.83/116.10 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 115.83/116.10 SPASS derived 80233 clauses, backtracked 0 clauses, performed 2 splits and kept 23923 clauses.
% 115.83/116.10 SPASS allocated 169637 KBytes.
% 115.83/116.10 SPASS spent 0:1:54.55 on the problem.
% 115.83/116.10 0:00:00.06 for the input.
% 115.83/116.10 0:00:00.00 for the FLOTTER CNF translation.
% 115.83/116.10 0:00:01.55 for inferences.
% 115.83/116.10 0:00:08.49 for the backtracking.
% 115.83/116.10 0:1:43.23 for the reduction.
% 115.83/116.10
% 115.83/116.10
% 115.83/116.10 Here is a proof with depth 5, length 44 :
% 115.83/116.10 % SZS output start Refutation
% See solution above
% 115.83/116.10 Formulae used in the proof : cls_ex__in__conv_0 cls_singletonE_0 cls_insert__not__empty_0 cls_set__empty2_1 cls_insert__commute_0 cls_keymode_Oinduct_0 cls_insert__absorb2_0 cls_insert__code_0 cls_distinct_Osimps_I1_J_0 cls_insert__code_1 cls_insertCI_1 cls_List_Oset_Osimps_I2_J_0 cls_distinct_Osimps_I2_J_0 cls_distinct_Osimps_I2_J_2 cls_set__ConsD_0 cls_not__Cons__self2_0 cls_mem__def_1 cls_conjecture_2
% 115.83/116.10
%------------------------------------------------------------------------------