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  
%------------------------------------------------------------------------------