%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV754-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 98.77s 98.95s
% Output : Refutation 98.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of clauses : 44 ( 26 unt; 7 nHn; 44 RR)
% Number of literals : 65 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(11,axiom,
~ hBOOL(c_in(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v)),
file('SWV754-1.p',unknown),
[] ).
cnf(25,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('SWV754-1.p',unknown),
[] ).
cnf(30,axiom,
~ equal(c_Set_Oinsert(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),
file('SWV754-1.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('SWV754-1.p',unknown),
[] ).
cnf(95,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('SWV754-1.p',unknown),
[] ).
cnf(114,axiom,
( ~ hBOOL(hAPP(u,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(u,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(u,v)) ),
file('SWV754-1.p',unknown),
[] ).
cnf(133,axiom,
equal(c_Set_Oinsert(u,c_Set_Oinsert(u,v,w),w),c_Set_Oinsert(u,v,w)),
file('SWV754-1.p',unknown),
[] ).
cnf(134,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,v,w),x))
| hBOOL(hAPP(v,x))
| equal(u,x) ),
file('SWV754-1.p',unknown),
[] ).
cnf(174,axiom,
c_List_Odistinct(c_List_Olist_ONil(u),u),
file('SWV754-1.p',unknown),
[] ).
cnf(184,axiom,
hBOOL(hAPP(c_Set_Oinsert(u,v,w),u)),
file('SWV754-1.p',unknown),
[] ).
cnf(245,axiom,
hBOOL(c_in(u,c_Set_Oinsert(u,v,w),w)),
file('SWV754-1.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('SWV754-1.p',unknown),
[] ).
cnf(448,axiom,
( ~ hBOOL(c_in(u,c_List_Oset(v,w),w))
| ~ c_List_Odistinct(c_List_Olist_OCons(u,v,w),w) ),
file('SWV754-1.p',unknown),
[] ).
cnf(450,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('SWV754-1.p',unknown),
[] ).
cnf(515,axiom,
~ equal(c_List_Olist_OCons(u,v,w),v),
file('SWV754-1.p',unknown),
[] ).
cnf(634,axiom,
( ~ hBOOL(hAPP(u,v))
| hBOOL(c_in(v,u,w)) ),
file('SWV754-1.p',unknown),
[] ).
cnf(987,plain,
~ hBOOL(c_in(u,c_List_Oset(c_List_Olist_ONil(v),v),v)),
inference(spl,[status(thm),theory(equality)],[51,11]),
[iquote('0:SpL:51.0,11.0')] ).
cnf(2941,plain,
hBOOL(hAPP(c_List_Oset(c_List_Olist_OCons(u,v,w),w),u)),
inference(spr,[status(thm),theory(equality)],[338,184]),
[iquote('0:SpR:338.0,184.0')] ).
cnf(2943,plain,
hBOOL(c_in(u,c_List_Oset(c_List_Olist_OCons(u,v,w),w),w)),
inference(spr,[status(thm),theory(equality)],[338,245]),
[iquote('0:SpR:338.0,245.0')] ).
cnf(2944,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)],[338,133]),
[iquote('0:SpR:338.0,133.0')] ).
cnf(3021,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)],[338,2944]),
[iquote('0:Rew:338.0,2944.0')] ).
cnf(3530,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)],[184,114]),
[iquote('0:Res:184.0,114.0')] ).
cnf(5333,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)],[634,25]),
[iquote('0:Res:634.1,25.0')] ).
cnf(5523,plain,
~ c_List_Odistinct(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),w),
inference(res,[status(thm),theory(equality)],[2943,448]),
[iquote('0:Res:2943.0,448.0')] ).
cnf(6488,plain,
hBOOL(hAPP(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),v)),
inference(spr,[status(thm),theory(equality)],[95,184]),
[iquote('0:SpR:95.0,184.0')] ).
cnf(10698,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)],[450,987]),
[iquote('0:Res:450.1,987.0')] ).
cnf(10709,plain,
c_List_Odistinct(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),v),
inference(mrr,[status(thm)],[10698,174]),
[iquote('0:MRR:10698.0,174.0')] ).
cnf(53730,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,c_List_Oset(c_List_Olist_ONil(v),v),v),w))
| equal(w,u) ),
inference(spl,[status(thm),theory(equality)],[51,5333]),
[iquote('0:SpL:51.0,5333.0')] ).
cnf(53738,plain,
( ~ hBOOL(hAPP(c_List_Oset(c_List_Olist_OCons(u,c_List_Olist_ONil(v),v),v),w))
| equal(w,u) ),
inference(rew,[status(thm),theory(equality)],[338,53730]),
[iquote('0:Rew:338.0,53730.0')] ).
cnf(60531,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)],[6488,3530]),
[iquote('0:Res:6488.0,3530.0')] ).
cnf(60533,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)],[95,60531]),
[iquote('0:Rew:95.0,60531.0')] ).
cnf(60720,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)],[60533,134]),
[iquote('0:Res:60533.0,134.0')] ).
cnf(60869,plain,
( equal(c_Public_Okeymode_OEncryption,u)
| equal(u,c_Public_Okeymode_OSignature) ),
inference(res,[status(thm),theory(equality)],[60720,5333]),
[iquote('0:Res:60720.0,5333.0')] ).
cnf(60961,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)],[60869,174]),
[iquote('0:SpR:60869.1,174.0')] ).
cnf(68213,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)],[60869,10709]),
[iquote('0:SpR:60869.1,10709.0')] ).
cnf(72181,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)],[60869,5523]),
[iquote('0:SpL:60869.1,5523.0')] ).
cnf(72648,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)],[60961,68213]),
[iquote('0:Rew:60961.0,68213.0')] ).
cnf(72649,plain,
c_List_Odistinct(c_Public_Okeymode_OSignature,u),
inference(mrr,[status(thm)],[72648,515]),
[iquote('0:MRR:72648.0,515.0')] ).
cnf(73980,plain,
equal(c_List_Olist_OCons(u,c_List_Olist_OCons(u,v,w),w),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[72181,72649]),
[iquote('0:MRR:72181.0,72649.0')] ).
cnf(73984,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)],[73980,3021]),
[iquote('0:Rew:73980.0,3021.0')] ).
cnf(74048,plain,
hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v)),
inference(rew,[status(thm),theory(equality)],[73984,2941]),
[iquote('0:Rew:73984.0,2941.0')] ).
cnf(74300,plain,
( ~ hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v))
| equal(v,w) ),
inference(rew,[status(thm),theory(equality)],[73984,53738]),
[iquote('0:Rew:73984.0,53738.0')] ).
cnf(74854,plain,
~ hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v)),
inference(aed,[status(thm),theory(equality)],[30,74300]),
[iquote('0:AED:30.0,74300.1')] ).
cnf(74855,plain,
$false,
inference(mrr,[status(thm)],[74854,74048]),
[iquote('0:MRR:74854.0,74048.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV754-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 15 09:39:40 EDT 2022
% 0.14/0.36 % CPUTime :
% 98.77/98.95
% 98.77/98.95 SPASS V 3.9
% 98.77/98.95 SPASS beiseite: Proof found.
% 98.77/98.95 % SZS status Theorem
% 98.77/98.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.77/98.95 SPASS derived 78808 clauses, backtracked 0 clauses, performed 0 splits and kept 23770 clauses.
% 98.77/98.95 SPASS allocated 158306 KBytes.
% 98.77/98.95 SPASS spent 0:1:37.02 on the problem.
% 98.77/98.95 0:00:00.06 for the input.
% 98.77/98.95 0:00:00.00 for the FLOTTER CNF translation.
% 98.77/98.95 0:00:01.45 for inferences.
% 98.77/98.95 0:00:00.00 for the backtracking.
% 98.77/98.95 0:1:34.37 for the reduction.
% 98.77/98.95
% 98.77/98.95
% 98.77/98.95 Here is a proof with depth 5, length 44 :
% 98.77/98.95 % SZS output start Refutation
% See solution above
% 98.77/98.95 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_not__Cons__self2_0 cls_mem__def_1
% 98.77/98.95
%------------------------------------------------------------------------------