TSTP Solution File: SWV752-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV752-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 21:45:01 EDT 2022
% Result : Unsatisfiable 85.45s 85.68s
% Output : Refutation 85.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of clauses : 48 ( 26 unt; 12 nHn; 48 RR)
% Number of literals : 73 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
~ c_in(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),
file('SWV752-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ hBOOL(hAPP(u,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(u,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(u,v)) ),
file('SWV752-1.p',unknown),
[] ).
cnf(41,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v)),
file('SWV752-1.p',unknown),
[] ).
cnf(63,axiom,
equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_List_Oset(c_List_Olist_ONil(u),u)),
file('SWV752-1.p',unknown),
[] ).
cnf(104,axiom,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u),
file('SWV752-1.p',unknown),
[] ).
cnf(122,axiom,
( c_in(u,v,w)
| c_in(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),w) ),
file('SWV752-1.p',unknown),
[] ).
cnf(123,axiom,
( ~ c_in(u,v,w)
| ~ c_in(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),w) ),
file('SWV752-1.p',unknown),
[] ).
cnf(167,axiom,
c_lessequals(u,c_Set_Oinsert(v,u,w),tc_fun(w,tc_bool)),
file('SWV752-1.p',unknown),
[] ).
cnf(223,axiom,
( ~ c_lessequals(c_Set_Oinsert(u,v,w),x,tc_fun(w,tc_bool))
| c_in(u,x,w) ),
file('SWV752-1.p',unknown),
[] ).
cnf(365,axiom,
( ~ c_in(u,v,w)
| equal(c_Set_Oinsert(u,v,w),v) ),
file('SWV752-1.p',unknown),
[] ).
cnf(384,axiom,
~ equal(c_List_Olist_OCons(u,v,w),v),
file('SWV752-1.p',unknown),
[] ).
cnf(414,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,v,w),x))
| hBOOL(hAPP(v,x))
| equal(u,x) ),
file('SWV752-1.p',unknown),
[] ).
cnf(427,axiom,
~ equal(c_List_Olist_OCons(u,v,w),c_List_Olist_ONil(w)),
file('SWV752-1.p',unknown),
[] ).
cnf(431,axiom,
hBOOL(hAPP(c_Set_Oinsert(u,v,w),u)),
file('SWV752-1.p',unknown),
[] ).
cnf(444,axiom,
equal(c_Set_Oinsert(u,c_List_Oset(v,w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
file('SWV752-1.p',unknown),
[] ).
cnf(534,axiom,
( ~ hBOOL(hAPP(u,v))
| c_in(v,u,w) ),
file('SWV752-1.p',unknown),
[] ).
cnf(535,axiom,
( ~ c_in(u,v,w)
| hBOOL(hAPP(v,u)) ),
file('SWV752-1.p',unknown),
[] ).
cnf(799,plain,
~ c_in(u,c_List_Oset(c_List_Olist_ONil(v),v),v),
inference(spl,[status(thm),theory(equality)],[63,16]),
[iquote('0:SpL:63.0,16.0')] ).
cnf(817,plain,
c_in(u,c_Set_Oinsert(u,v,w),x),
inference(res,[status(thm),theory(equality)],[431,534]),
[iquote('0:Res:431.0,534.0')] ).
cnf(1201,plain,
( ~ c_in(u,v,w)
| c_in(u,v,x) ),
inference(spr,[status(thm),theory(equality)],[365,817]),
[iquote('0:SpR:365.1,817.0')] ).
cnf(1743,plain,
( c_in(u,v,w)
| hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),u)) ),
inference(res,[status(thm),theory(equality)],[122,535]),
[iquote('0:Res:122.1,535.0')] ).
cnf(1835,plain,
( c_in(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),w)
| hBOOL(hAPP(v,u)) ),
inference(spr,[status(thm),theory(equality)],[104,1743]),
[iquote('0:SpR:104.0,1743.1')] ).
cnf(1849,plain,
( hBOOL(hAPP(u,v))
| c_in(v,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x) ),
inference(res,[status(thm),theory(equality)],[1835,1201]),
[iquote('0:Res:1835.0,1201.0')] ).
cnf(1860,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w))
| c_in(w,u,x) ),
inference(spr,[status(thm),theory(equality)],[104,1849]),
[iquote('0:SpR:104.0,1849.1')] ).
cnf(1893,plain,
hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_List_Oset(c_List_Olist_ONil(u),u),tc_fun(v,tc_bool)),w)),
inference(res,[status(thm),theory(equality)],[1860,799]),
[iquote('0:Res:1860.1,799.0')] ).
cnf(1903,plain,
c_in(u,c_HOL_Ouminus__class_Ouminus(c_List_Oset(c_List_Olist_ONil(v),v),tc_fun(w,tc_bool)),x),
inference(res,[status(thm),theory(equality)],[1893,534]),
[iquote('0:Res:1893.0,534.0')] ).
cnf(2703,plain,
c_in(u,c_List_Oset(c_List_Olist_OCons(u,v,w),w),x),
inference(spr,[status(thm),theory(equality)],[444,817]),
[iquote('0:SpR:444.0,817.0')] ).
cnf(3183,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)],[431,29]),
[iquote('0:Res:431.0,29.0')] ).
cnf(3840,plain,
~ c_in(u,c_List_Oset(c_List_Olist_ONil(v),v),w),
inference(res,[status(thm),theory(equality)],[1903,123]),
[iquote('0:Res:1903.0,123.1')] ).
cnf(4196,plain,
c_in(u,c_Set_Oinsert(v,c_Set_Oinsert(u,w,x),x),x),
inference(res,[status(thm),theory(equality)],[167,223]),
[iquote('0:Res:167.0,223.0')] ).
cnf(4614,plain,
c_in(u,c_Set_Oinsert(v,c_Set_Oinsert(u,w,x),x),y),
inference(res,[status(thm),theory(equality)],[4196,1201]),
[iquote('0:Res:4196.0,1201.0')] ).
cnf(4616,plain,
hBOOL(hAPP(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),v)),
inference(res,[status(thm),theory(equality)],[4196,535]),
[iquote('0:Res:4196.0,535.0')] ).
cnf(4656,plain,
c_in(u,c_Set_Oinsert(v,c_List_Oset(c_List_Olist_OCons(u,w,x),x),x),y),
inference(spr,[status(thm),theory(equality)],[444,4614]),
[iquote('0:SpR:444.0,4614.0')] ).
cnf(4668,plain,
c_in(u,c_List_Oset(c_List_Olist_OCons(v,c_List_Olist_OCons(u,w,x),x),x),y),
inference(rew,[status(thm),theory(equality)],[444,4656]),
[iquote('0:Rew:444.0,4656.0')] ).
cnf(55208,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)],[4616,3183]),
[iquote('0:Res:4616.0,3183.0')] ).
cnf(55246,plain,
( hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,u,v),w))
| equal(c_Public_Okeymode_OSignature,w) ),
inference(res,[status(thm),theory(equality)],[55208,414]),
[iquote('0:Res:55208.0,414.0')] ).
cnf(55365,plain,
( equal(c_Public_Okeymode_OSignature,u)
| hBOOL(hAPP(v,u))
| equal(c_Public_Okeymode_OEncryption,u) ),
inference(res,[status(thm),theory(equality)],[55246,414]),
[iquote('0:Res:55246.0,414.0')] ).
cnf(55378,plain,
( equal(c_Public_Okeymode_OSignature,u)
| equal(c_Public_Okeymode_OEncryption,u) ),
inference(res,[status(thm),theory(equality)],[55365,41]),
[iquote('0:Res:55365.1,41.0')] ).
cnf(60138,plain,
( equal(c_List_Olist_OCons(u,v,w),c_Public_Okeymode_OSignature)
| c_in(u,c_List_Oset(c_Public_Okeymode_OEncryption,w),x) ),
inference(spr,[status(thm),theory(equality)],[55378,2703]),
[iquote('0:SpR:55378.1,2703.0')] ).
cnf(60192,plain,
( equal(c_List_Olist_OCons(u,c_List_Olist_OCons(v,w,x),x),c_Public_Okeymode_OSignature)
| c_in(v,c_List_Oset(c_Public_Okeymode_OEncryption,x),y) ),
inference(spr,[status(thm),theory(equality)],[55378,4668]),
[iquote('0:SpR:55378.1,4668.0')] ).
cnf(61721,plain,
( ~ c_in(u,c_List_Oset(c_Public_Okeymode_OEncryption,v),w)
| equal(c_List_Olist_ONil(v),c_Public_Okeymode_OSignature) ),
inference(spl,[status(thm),theory(equality)],[55378,3840]),
[iquote('0:SpL:55378.1,3840.0')] ).
cnf(62532,plain,
( ~ equal(c_Public_Okeymode_OEncryption,u)
| equal(c_List_Olist_OCons(v,u,w),c_Public_Okeymode_OSignature) ),
inference(spl,[status(thm),theory(equality)],[55378,384]),
[iquote('0:SpL:55378.1,384.0')] ).
cnf(64620,plain,
( equal(c_List_Olist_OCons(u,c_Public_Okeymode_OSignature,v),c_Public_Okeymode_OSignature)
| c_in(w,c_List_Oset(c_Public_Okeymode_OEncryption,v),x) ),
inference(rew,[status(thm),theory(equality)],[60138,60192]),
[iquote('0:Rew:60138.0,60192.0')] ).
cnf(64621,plain,
c_in(u,c_List_Oset(c_Public_Okeymode_OEncryption,v),w),
inference(mrr,[status(thm)],[64620,384]),
[iquote('0:MRR:64620.0,384.0')] ).
cnf(64622,plain,
equal(c_List_Olist_ONil(u),c_Public_Okeymode_OSignature),
inference(mrr,[status(thm)],[61721,64621]),
[iquote('0:MRR:61721.0,64621.0')] ).
cnf(64670,plain,
~ equal(c_List_Olist_OCons(u,v,w),c_Public_Okeymode_OSignature),
inference(rew,[status(thm),theory(equality)],[64622,427]),
[iquote('0:Rew:64622.0,427.0')] ).
cnf(65271,plain,
~ equal(c_Public_Okeymode_OEncryption,u),
inference(mrr,[status(thm)],[62532,64670]),
[iquote('0:MRR:62532.1,64670.0')] ).
cnf(65334,plain,
$false,
inference(obv,[status(thm),theory(equality)],[65271]),
[iquote('0:Obv:65271.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV752-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n016.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 02:05:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 85.45/85.68
% 85.45/85.68 SPASS V 3.9
% 85.45/85.68 SPASS beiseite: Proof found.
% 85.45/85.68 % SZS status Theorem
% 85.45/85.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 85.45/85.68 SPASS derived 52334 clauses, backtracked 0 clauses, performed 0 splits and kept 19720 clauses.
% 85.45/85.68 SPASS allocated 135573 KBytes.
% 85.45/85.68 SPASS spent 0:1:24.51 on the problem.
% 85.45/85.68 0:00:00.06 for the input.
% 85.45/85.68 0:00:00.00 for the FLOTTER CNF translation.
% 85.45/85.68 0:00:01.50 for inferences.
% 85.45/85.68 0:00:00.00 for the backtracking.
% 85.45/85.68 0:1:21.98 for the reduction.
% 85.45/85.68
% 85.45/85.68
% 85.45/85.68 Here is a proof with depth 8, length 48 :
% 85.45/85.68 % SZS output start Refutation
% See solution above
% 85.45/85.68 Formulae used in the proof : cls_ex__in__conv_0 cls_keymode_Oinduct_0 cls_bot1E_0 cls_set__empty2_1 cls_double__complement_0 cls_ComplI_0 cls_ComplD_0 cls_subset__insertI_0 cls_insert__subset_0 cls_insert__absorb_0 cls_not__Cons__self2_0 cls_insert__code_0 cls_list_Osimps_I2_J_0 cls_insert__code_1 cls_List_Oset_Osimps_I2_J_0 cls_mem__def_1 cls_mem__def_0
% 85.45/85.68
%------------------------------------------------------------------------------