TSTP Solution File: SWV731-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV731-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 21:44:56 EDT 2022
% Result : Unsatisfiable 89.55s 89.81s
% Output : Refutation 89.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 19 unt; 6 nHn; 32 RR)
% Number of literals : 47 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 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(15,axiom,
( ~ hBOOL(hAPP(u,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(u,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(u,v)) ),
file('SWV731-1.p',unknown),
[] ).
cnf(71,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v)),
file('SWV731-1.p',unknown),
[] ).
cnf(244,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(u),v),c_Set_Oinsert(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),u)))
| equal(v,w) ),
file('SWV731-1.p',unknown),
[] ).
cnf(258,axiom,
equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_List_Oset(c_List_Olist_ONil(u),u)),
file('SWV731-1.p',unknown),
[] ).
cnf(444,axiom,
~ equal(c_List_Olist_OCons(u,v,w),v),
file('SWV731-1.p',unknown),
[] ).
cnf(458,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('SWV731-1.p',unknown),
[] ).
cnf(470,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,v,w),x))
| hBOOL(hAPP(v,x))
| equal(u,x) ),
file('SWV731-1.p',unknown),
[] ).
cnf(477,axiom,
~ equal(c_List_Olist_OCons(u,v,w),c_List_Olist_ONil(w)),
file('SWV731-1.p',unknown),
[] ).
cnf(484,axiom,
hBOOL(hAPP(c_Set_Oinsert(u,v,w),u)),
file('SWV731-1.p',unknown),
[] ).
cnf(498,axiom,
equal(c_Set_Oinsert(u,c_List_Oset(v,w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
file('SWV731-1.p',unknown),
[] ).
cnf(584,axiom,
( ~ hBOOL(hAPP(u,v))
| hBOOL(hAPP(hAPP(c_in(w),v),u)) ),
file('SWV731-1.p',unknown),
[] ).
cnf(852,plain,
~ hBOOL(hAPP(c_List_Oset(c_List_Olist_ONil(u),u),v)),
inference(spl,[status(thm),theory(equality)],[258,71]),
[iquote('0:SpL:258.0,71.0')] ).
cnf(2187,plain,
hBOOL(hAPP(c_List_Oset(c_List_Olist_OCons(u,v,w),w),u)),
inference(spr,[status(thm),theory(equality)],[498,484]),
[iquote('0:SpR:498.0,484.0')] ).
cnf(2638,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)],[484,15]),
[iquote('0:Res:484.0,15.0')] ).
cnf(4802,plain,
hBOOL(hAPP(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),v)),
inference(spr,[status(thm),theory(equality)],[458,484]),
[iquote('0:SpR:458.0,484.0')] ).
cnf(5048,plain,
hBOOL(hAPP(c_Set_Oinsert(u,c_List_Oset(c_List_Olist_OCons(v,w,x),x),x),v)),
inference(spr,[status(thm),theory(equality)],[498,4802]),
[iquote('0:SpR:498.0,4802.0')] ).
cnf(5074,plain,
hBOOL(hAPP(c_List_Oset(c_List_Olist_OCons(u,c_List_Olist_OCons(v,w,x),x),x),v)),
inference(rew,[status(thm),theory(equality)],[498,5048]),
[iquote('0:Rew:498.0,5048.0')] ).
cnf(8639,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)],[584,244]),
[iquote('0:Res:584.1,244.0')] ).
cnf(57812,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)],[4802,2638]),
[iquote('0:Res:4802.0,2638.0')] ).
cnf(57813,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)],[458,57812]),
[iquote('0:Rew:458.0,57812.0')] ).
cnf(57835,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)],[57813,470]),
[iquote('0:Res:57813.0,470.0')] ).
cnf(57871,plain,
( equal(c_Public_Okeymode_OEncryption,u)
| equal(u,c_Public_Okeymode_OSignature) ),
inference(res,[status(thm),theory(equality)],[57835,8639]),
[iquote('0:Res:57835.0,8639.0')] ).
cnf(63608,plain,
( equal(c_List_Olist_OCons(u,v,w),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OSignature,w),u)) ),
inference(spr,[status(thm),theory(equality)],[57871,2187]),
[iquote('0:SpR:57871.1,2187.0')] ).
cnf(63677,plain,
( equal(c_List_Olist_OCons(u,c_List_Olist_OCons(v,w,x),x),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OSignature,x),v)) ),
inference(spr,[status(thm),theory(equality)],[57871,5074]),
[iquote('0:SpR:57871.1,5074.0')] ).
cnf(64554,plain,
( ~ hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OSignature,u),v))
| equal(c_List_Olist_ONil(u),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[57871,852]),
[iquote('0:SpL:57871.1,852.0')] ).
cnf(66277,plain,
( ~ equal(c_Public_Okeymode_OSignature,u)
| equal(c_List_Olist_OCons(v,u,w),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[57871,444]),
[iquote('0:SpL:57871.1,444.0')] ).
cnf(67622,plain,
( equal(c_List_Olist_OCons(u,c_Public_Okeymode_OEncryption,v),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OSignature,v),w)) ),
inference(rew,[status(thm),theory(equality)],[63608,63677]),
[iquote('0:Rew:63608.0,63677.0')] ).
cnf(67623,plain,
hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OSignature,u),v)),
inference(mrr,[status(thm)],[67622,444]),
[iquote('0:MRR:67622.0,444.0')] ).
cnf(67624,plain,
equal(c_List_Olist_ONil(u),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[64554,67623]),
[iquote('0:MRR:64554.0,67623.0')] ).
cnf(67704,plain,
~ equal(c_List_Olist_OCons(u,v,w),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[67624,477]),
[iquote('0:Rew:67624.0,477.0')] ).
cnf(68452,plain,
~ equal(c_Public_Okeymode_OSignature,u),
inference(mrr,[status(thm)],[66277,67704]),
[iquote('0:MRR:66277.1,67704.0')] ).
cnf(68483,plain,
$false,
inference(obv,[status(thm),theory(equality)],[68452]),
[iquote('0:Obv:68452.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV731-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 22:53:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 89.55/89.81
% 89.55/89.81 SPASS V 3.9
% 89.55/89.81 SPASS beiseite: Proof found.
% 89.55/89.81 % SZS status Theorem
% 89.55/89.81 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 89.55/89.81 SPASS derived 58753 clauses, backtracked 0 clauses, performed 0 splits and kept 24002 clauses.
% 89.55/89.81 SPASS allocated 150154 KBytes.
% 89.55/89.81 SPASS spent 0:1:28.36 on the problem.
% 89.55/89.81 0:00:00.06 for the input.
% 89.55/89.81 0:00:00.00 for the FLOTTER CNF translation.
% 89.55/89.81 0:00:01.16 for inferences.
% 89.55/89.81 0:00:00.00 for the backtracking.
% 89.55/89.81 0:1:26.33 for the reduction.
% 89.55/89.81
% 89.55/89.81
% 89.55/89.81 Here is a proof with depth 5, length 32 :
% 89.55/89.81 % SZS output start Refutation
% See solution above
% 89.55/89.81 Formulae used in the proof : cls_keymode_Oinduct_0 cls_bot1E_0 cls_singletonE_0 cls_set__empty2_1 cls_not__Cons__self2_0 cls_insert__commute_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
% 89.55/89.81
%------------------------------------------------------------------------------