TSTP Solution File: SWV742-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV742-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 21:44:59 EDT 2022
% Result : Unsatisfiable 163.38s 163.59s
% Output : Refutation 163.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 31 ( 18 unt; 6 nHn; 31 RR)
% Number of literals : 46 ( 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(31,axiom,
( ~ hBOOL(hAPP(u,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(u,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(u,v)) ),
file('SWV742-1.p',unknown),
[] ).
cnf(43,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v)),
file('SWV742-1.p',unknown),
[] ).
cnf(61,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('SWV742-1.p',unknown),
[] ).
cnf(65,axiom,
equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_List_Oset(c_List_Olist_ONil(u),u)),
file('SWV742-1.p',unknown),
[] ).
cnf(410,axiom,
~ equal(c_List_Olist_OCons(u,v,w),v),
file('SWV742-1.p',unknown),
[] ).
cnf(423,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('SWV742-1.p',unknown),
[] ).
cnf(438,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,v,w),x))
| hBOOL(hAPP(v,x))
| equal(u,x) ),
file('SWV742-1.p',unknown),
[] ).
cnf(451,axiom,
~ equal(c_List_Olist_OCons(u,v,w),c_List_Olist_ONil(w)),
file('SWV742-1.p',unknown),
[] ).
cnf(455,axiom,
hBOOL(hAPP(c_Set_Oinsert(u,v,w),u)),
file('SWV742-1.p',unknown),
[] ).
cnf(465,axiom,
equal(c_Set_Oinsert(u,c_List_Oset(v,w),w),c_List_Oset(c_List_Olist_OCons(u,v,w),w)),
file('SWV742-1.p',unknown),
[] ).
cnf(554,axiom,
( ~ hBOOL(hAPP(u,v))
| hBOOL(c_in(v,u,w)) ),
file('SWV742-1.p',unknown),
[] ).
cnf(892,plain,
~ hBOOL(hAPP(c_List_Oset(c_List_Olist_ONil(u),u),v)),
inference(spl,[status(thm),theory(equality)],[65,43]),
[iquote('0:SpL:65.0,43.0')] ).
cnf(2350,plain,
hBOOL(hAPP(c_List_Oset(c_List_Olist_OCons(u,v,w),w),u)),
inference(spr,[status(thm),theory(equality)],[465,455]),
[iquote('0:SpR:465.0,455.0')] ).
cnf(3007,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)],[455,31]),
[iquote('0:Res:455.0,31.0')] ).
cnf(5494,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)],[554,61]),
[iquote('0:Res:554.1,61.0')] ).
cnf(6583,plain,
hBOOL(hAPP(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),v)),
inference(spr,[status(thm),theory(equality)],[423,455]),
[iquote('0:SpR:423.0,455.0')] ).
cnf(6780,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)],[465,6583]),
[iquote('0:SpR:465.0,6583.0')] ).
cnf(6798,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)],[465,6780]),
[iquote('0:Rew:465.0,6780.0')] ).
cnf(64136,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)],[6583,3007]),
[iquote('0:Res:6583.0,3007.0')] ).
cnf(64153,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)],[64136,438]),
[iquote('0:Res:64136.0,438.0')] ).
cnf(64200,plain,
( equal(c_Public_Okeymode_OSignature,u)
| equal(u,c_Public_Okeymode_OEncryption) ),
inference(res,[status(thm),theory(equality)],[64153,5494]),
[iquote('0:Res:64153.0,5494.0')] ).
cnf(70211,plain,
( equal(c_List_Olist_OCons(u,v,w),c_Public_Okeymode_OSignature)
| hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,w),u)) ),
inference(spr,[status(thm),theory(equality)],[64200,2350]),
[iquote('0:SpR:64200.1,2350.0')] ).
cnf(70292,plain,
( equal(c_List_Olist_OCons(u,c_List_Olist_OCons(v,w,x),x),c_Public_Okeymode_OSignature)
| hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,x),v)) ),
inference(spr,[status(thm),theory(equality)],[64200,6798]),
[iquote('0:SpR:64200.1,6798.0')] ).
cnf(71493,plain,
( ~ hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v))
| equal(c_List_Olist_ONil(u),c_Public_Okeymode_OSignature) ),
inference(spl,[status(thm),theory(equality)],[64200,892]),
[iquote('0:SpL:64200.1,892.0')] ).
cnf(72889,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)],[64200,410]),
[iquote('0:SpL:64200.1,410.0')] ).
cnf(74321,plain,
( equal(c_List_Olist_OCons(u,c_Public_Okeymode_OSignature,v),c_Public_Okeymode_OSignature)
| hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,v),w)) ),
inference(rew,[status(thm),theory(equality)],[70211,70292]),
[iquote('0:Rew:70211.0,70292.0')] ).
cnf(74322,plain,
hBOOL(hAPP(c_List_Oset(c_Public_Okeymode_OEncryption,u),v)),
inference(mrr,[status(thm)],[74321,410]),
[iquote('0:MRR:74321.0,410.0')] ).
cnf(74323,plain,
equal(c_List_Olist_ONil(u),c_Public_Okeymode_OSignature),
inference(mrr,[status(thm)],[71493,74322]),
[iquote('0:MRR:71493.0,74322.0')] ).
cnf(74441,plain,
~ equal(c_List_Olist_OCons(u,v,w),c_Public_Okeymode_OSignature),
inference(rew,[status(thm),theory(equality)],[74323,451]),
[iquote('0:Rew:74323.0,451.0')] ).
cnf(75369,plain,
~ equal(c_Public_Okeymode_OEncryption,u),
inference(mrr,[status(thm)],[72889,74441]),
[iquote('0:MRR:72889.1,74441.0')] ).
cnf(75402,plain,
$false,
inference(obv,[status(thm),theory(equality)],[75369]),
[iquote('0:Obv:75369.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV742-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 11:55:11 EDT 2022
% 0.13/0.35 % CPUTime :
% 163.38/163.59
% 163.38/163.59 SPASS V 3.9
% 163.38/163.59 SPASS beiseite: Proof found.
% 163.38/163.59 % SZS status Theorem
% 163.38/163.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 163.38/163.59 SPASS derived 78351 clauses, backtracked 0 clauses, performed 0 splits and kept 30694 clauses.
% 163.38/163.59 SPASS allocated 168925 KBytes.
% 163.38/163.59 SPASS spent 0:2:41.94 on the problem.
% 163.38/163.59 0:00:00.06 for the input.
% 163.38/163.59 0:00:00.00 for the FLOTTER CNF translation.
% 163.38/163.59 0:00:01.14 for inferences.
% 163.38/163.59 0:00:00.00 for the backtracking.
% 163.38/163.59 0:2:39.94 for the reduction.
% 163.38/163.59
% 163.38/163.59
% 163.38/163.59 Here is a proof with depth 5, length 31 :
% 163.38/163.59 % SZS output start Refutation
% See solution above
% 163.38/163.59 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
% 163.38/163.59
%------------------------------------------------------------------------------