TSTP Solution File: SCT168+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SCT168+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Mon Mar 7 00:25:28 EST 2011
% Result : Theorem 28.98s
% Output : Solution 28.98s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP13847/SCT168+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% WARNING: TreeLimitedRun lost 0.13s, total lost is 0.13s
% found
% SZS status THM for /tmp/SystemOnTPTP13847/SCT168+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP13847/SCT168+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=60 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 13971
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.01 WC
% PrfWatch: 1.92 CPU 2.01 WC
% PrfWatch: 3.91 CPU 4.02 WC
% PrfWatch: 5.90 CPU 6.02 WC
% PrfWatch: 7.89 CPU 8.03 WC
% # Preprocessing time : 0.133 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 9.88 CPU 10.03 WC
% PrfWatch: 11.87 CPU 12.04 WC
% # SZS output start CNFRefutation.
% fof(4, axiom,![X1]:![X2]:![X3]:(hBOOL(hAPP(hAPP(c_member(X3),X2),X1))<=>hBOOL(hAPP(X1,X2))),file('/tmp/SRASS.s.p', fact_mem__def)).
% fof(7, axiom,![X7]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7),X7))),file('/tmp/SRASS.s.p', fact_less__irrefl__nat)).
% fof(58, axiom,![X37]:(c_Finite__Set_Ofinite(tc_Nat_Onat,X37)<=>?[X36]:![X30]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30),X37))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X36)))),file('/tmp/SRASS.s.p', fact_finite__nat__set__iff__bounded)).
% fof(70, axiom,![X14]:![X2]:(~(X2=X14)|hBOOL(hAPP(hAPP(c_fequal,X2),X14))),file('/tmp/SRASS.s.p', help_c__fequal__2)).
% fof(99, axiom,![X10]:![X38]:![X18]:![X3]:![X46]:![X11]:hAPP(c_COMBS(X11,X46,X3,X18,X38),X10)=hAPP(hAPP(X18,X10),hAPP(X38,X10)),file('/tmp/SRASS.s.p', help_c__COMBS__1)).
% fof(120, axiom,![X7]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7),X7)),file('/tmp/SRASS.s.p', fact_le__refl)).
% fof(137, axiom,![X11]:![X2]:![X21]:![X3]:hBOOL(hAPP(hAPP(c_member(X3),hAPP(X21,X2)),c_Set_Oimage(X11,X3,X21,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool))))),file('/tmp/SRASS.s.p', fact_rangeI)).
% fof(167, axiom,![X1]:![X3]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),file('/tmp/SRASS.s.p', fact_subset__UNIV)).
% fof(168, axiom,![X1]:![X5]:![X3]:(c_Finite__Set_Ofinite(X3,X5)=>(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1),X5))=>c_Finite__Set_Ofinite(X3,X1))),file('/tmp/SRASS.s.p', fact_rev__finite__subset)).
% fof(235, axiom,![X21]:![X5]:![X11]:![X1]:![X3]:(c_Finite__Set_Ofinite(X3,X1)=>(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11,tc_HOL_Obool),X5),c_Set_Oimage(X3,X11,X21,X1)))=>c_Finite__Set_Ofinite(X11,X5))),file('/tmp/SRASS.s.p', fact_finite__surj)).
% fof(243, axiom,class_Orderings_Oord(tc_HOL_Obool),file('/tmp/SRASS.s.p', arity_HOL__Obool__Orderings_Oord)).
% fof(251, axiom,![X1]:![X3]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X3,X1)))=>c_Finite__Set_Ofinite(X3,X1)),file('/tmp/SRASS.s.p', fact_card__ge__0__finite)).
% fof(344, axiom,![X21]:![X3]:![X11]:(c_Set_Oimage(X11,X3,X21,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))<=>![X30]:hAPP(X21,hAPP(c_Hilbert__Choice_Oinv__into(X11,X3,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)),X21),X30))=X30),file('/tmp/SRASS.s.p', fact_surj__iff__all)).
% fof(356, axiom,![X69]:![X3]:hAPP(c_COMBI(X3),X69)=X69,file('/tmp/SRASS.s.p', help_c__COMBI__1)).
% fof(360, axiom,![X55]:![X21]:![X3]:![X11]:(class_Orderings_Oord(X11)=>(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X11),X21),X55))<=>![X30]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X11,hAPP(X21,X30)),hAPP(X55,X30))))),file('/tmp/SRASS.s.p', fact_le__fun__def)).
% fof(393, axiom,![X22]:hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22)=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22)),file('/tmp/SRASS.s.p', fact_less__eq__Suc__le__raw)).
% fof(414, axiom,c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat),file('/tmp/SRASS.s.p', fact_card__UNIV__unit)).
% fof(450, axiom,![X1]:![X21]:![X11]:![X14]:![X3]:(hBOOL(hAPP(hAPP(c_member(X3),X14),c_Set_Oimage(X11,X3,X21,X1)))=>hAPP(X21,hAPP(c_Hilbert__Choice_Oinv__into(X11,X3,X1,X21),X14))=X14),file('/tmp/SRASS.s.p', fact_f__inv__into__f)).
% fof(458, axiom,c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),file('/tmp/SRASS.s.p', fact_One__nat__def)).
% fof(535, plain,![X7]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7),X7))),inference(fof_simplification,[status(thm)],[7,theory(equality)])).
% fof(606, plain,![X1]:![X2]:![X3]:((~(hBOOL(hAPP(hAPP(c_member(X3),X2),X1)))|hBOOL(hAPP(X1,X2)))&(~(hBOOL(hAPP(X1,X2)))|hBOOL(hAPP(hAPP(c_member(X3),X2),X1)))),inference(fof_nnf,[status(thm)],[4])).
% fof(607, plain,![X4]:![X5]:![X6]:((~(hBOOL(hAPP(hAPP(c_member(X6),X5),X4)))|hBOOL(hAPP(X4,X5)))&(~(hBOOL(hAPP(X4,X5)))|hBOOL(hAPP(hAPP(c_member(X6),X5),X4)))),inference(variable_rename,[status(thm)],[606])).
% cnf(608,plain,(hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X3,X2))),inference(split_conjunct,[status(thm)],[607])).
% fof(616, plain,![X8]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X8))),inference(variable_rename,[status(thm)],[535])).
% cnf(617,plain,(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1))),inference(split_conjunct,[status(thm)],[616])).
% fof(897, plain,![X37]:((~(c_Finite__Set_Ofinite(tc_Nat_Onat,X37))|?[X36]:![X30]:(~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30),X37)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X36))))&(![X36]:?[X30]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30),X37))&~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X36))))|c_Finite__Set_Ofinite(tc_Nat_Onat,X37))),inference(fof_nnf,[status(thm)],[58])).
% fof(898, plain,![X38]:((~(c_Finite__Set_Ofinite(tc_Nat_Onat,X38))|?[X39]:![X40]:(~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X40),X38)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X40),X39))))&(![X41]:?[X42]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X42),X38))&~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X41))))|c_Finite__Set_Ofinite(tc_Nat_Onat,X38))),inference(variable_rename,[status(thm)],[897])).
% fof(899, plain,![X38]:((~(c_Finite__Set_Ofinite(tc_Nat_Onat,X38))|![X40]:(~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X40),X38)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X40),esk16_1(X38)))))&(![X41]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk17_2(X38,X41)),X38))&~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk17_2(X38,X41)),X41))))|c_Finite__Set_Ofinite(tc_Nat_Onat,X38))),inference(skolemize,[status(esa)],[898])).
% fof(900, plain,![X38]:![X40]:![X41]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk17_2(X38,X41)),X38))&~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk17_2(X38,X41)),X41))))|c_Finite__Set_Ofinite(tc_Nat_Onat,X38))&((~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X40),X38)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X40),esk16_1(X38))))|~(c_Finite__Set_Ofinite(tc_Nat_Onat,X38)))),inference(shift_quantors,[status(thm)],[899])).
% fof(901, plain,![X38]:![X40]:![X41]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk17_2(X38,X41)),X38))|c_Finite__Set_Ofinite(tc_Nat_Onat,X38))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk17_2(X38,X41)),X41)))|c_Finite__Set_Ofinite(tc_Nat_Onat,X38)))&((~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X40),X38)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X40),esk16_1(X38))))|~(c_Finite__Set_Ofinite(tc_Nat_Onat,X38)))),inference(distribute,[status(thm)],[900])).
% cnf(902,plain,(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk16_1(X1)))|~c_Finite__Set_Ofinite(tc_Nat_Onat,X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1))),inference(split_conjunct,[status(thm)],[901])).
% fof(937, plain,![X15]:![X16]:(~(X16=X15)|hBOOL(hAPP(hAPP(c_fequal,X16),X15))),inference(variable_rename,[status(thm)],[70])).
% cnf(938,plain,(hBOOL(hAPP(hAPP(c_fequal,X1),X2))|X1!=X2),inference(split_conjunct,[status(thm)],[937])).
% fof(1079, plain,![X47]:![X48]:![X49]:![X50]:![X51]:![X52]:hAPP(c_COMBS(X52,X51,X50,X49,X48),X47)=hAPP(hAPP(X49,X47),hAPP(X48,X47)),inference(variable_rename,[status(thm)],[99])).
% cnf(1080,plain,(hAPP(c_COMBS(X1,X2,X3,X4,X5),X6)=hAPP(hAPP(X4,X6),hAPP(X5,X6))),inference(split_conjunct,[status(thm)],[1079])).
% fof(1149, plain,![X8]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),X8)),inference(variable_rename,[status(thm)],[120])).
% cnf(1150,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1))),inference(split_conjunct,[status(thm)],[1149])).
% fof(1227, plain,![X22]:![X23]:![X24]:![X25]:hBOOL(hAPP(hAPP(c_member(X25),hAPP(X24,X23)),c_Set_Oimage(X22,X25,X24,c_Orderings_Otop__class_Otop(tc_fun(X22,tc_HOL_Obool))))),inference(variable_rename,[status(thm)],[137])).
% cnf(1228,plain,(hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))),inference(split_conjunct,[status(thm)],[1227])).
% fof(1311, plain,![X4]:![X5]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),inference(variable_rename,[status(thm)],[167])).
% cnf(1312,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),inference(split_conjunct,[status(thm)],[1311])).
% fof(1313, plain,![X1]:![X5]:![X3]:(~(c_Finite__Set_Ofinite(X3,X5))|(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1),X5)))|c_Finite__Set_Ofinite(X3,X1))),inference(fof_nnf,[status(thm)],[168])).
% fof(1314, plain,![X6]:![X7]:![X8]:(~(c_Finite__Set_Ofinite(X8,X7))|(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X6),X7)))|c_Finite__Set_Ofinite(X8,X6))),inference(variable_rename,[status(thm)],[1313])).
% cnf(1315,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))|~c_Finite__Set_Ofinite(X1,X3)),inference(split_conjunct,[status(thm)],[1314])).
% fof(1573, plain,![X21]:![X5]:![X11]:![X1]:![X3]:(~(c_Finite__Set_Ofinite(X3,X1))|(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11,tc_HOL_Obool),X5),c_Set_Oimage(X3,X11,X21,X1))))|c_Finite__Set_Ofinite(X11,X5))),inference(fof_nnf,[status(thm)],[235])).
% fof(1574, plain,![X22]:![X23]:![X24]:![X25]:![X26]:(~(c_Finite__Set_Ofinite(X26,X25))|(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24,tc_HOL_Obool),X23),c_Set_Oimage(X26,X24,X22,X25))))|c_Finite__Set_Ofinite(X24,X23))),inference(variable_rename,[status(thm)],[1573])).
% cnf(1575,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))|~c_Finite__Set_Ofinite(X3,X5)),inference(split_conjunct,[status(thm)],[1574])).
% cnf(1590,plain,(class_Orderings_Oord(tc_HOL_Obool)),inference(split_conjunct,[status(thm)],[243])).
% fof(1612, plain,![X1]:![X3]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X3,X1))))|c_Finite__Set_Ofinite(X3,X1)),inference(fof_nnf,[status(thm)],[251])).
% fof(1613, plain,![X4]:![X5]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X5,X4))))|c_Finite__Set_Ofinite(X5,X4)),inference(variable_rename,[status(thm)],[1612])).
% cnf(1614,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,X2)))),inference(split_conjunct,[status(thm)],[1613])).
% fof(1868, plain,![X21]:![X3]:![X11]:((~(c_Set_Oimage(X11,X3,X21,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))|![X30]:hAPP(X21,hAPP(c_Hilbert__Choice_Oinv__into(X11,X3,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)),X21),X30))=X30)&(?[X30]:~(hAPP(X21,hAPP(c_Hilbert__Choice_Oinv__into(X11,X3,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)),X21),X30))=X30)|c_Set_Oimage(X11,X3,X21,c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),inference(fof_nnf,[status(thm)],[344])).
% fof(1869, plain,![X31]:![X32]:![X33]:((~(c_Set_Oimage(X33,X32,X31,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X32,tc_HOL_Obool)))|![X34]:hAPP(X31,hAPP(c_Hilbert__Choice_Oinv__into(X33,X32,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)),X31),X34))=X34)&(?[X35]:~(hAPP(X31,hAPP(c_Hilbert__Choice_Oinv__into(X33,X32,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)),X31),X35))=X35)|c_Set_Oimage(X33,X32,X31,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X32,tc_HOL_Obool)))),inference(variable_rename,[status(thm)],[1868])).
% fof(1870, plain,![X31]:![X32]:![X33]:((~(c_Set_Oimage(X33,X32,X31,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X32,tc_HOL_Obool)))|![X34]:hAPP(X31,hAPP(c_Hilbert__Choice_Oinv__into(X33,X32,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)),X31),X34))=X34)&(~(hAPP(X31,hAPP(c_Hilbert__Choice_Oinv__into(X33,X32,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)),X31),esk42_3(X31,X32,X33)))=esk42_3(X31,X32,X33))|c_Set_Oimage(X33,X32,X31,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X32,tc_HOL_Obool)))),inference(skolemize,[status(esa)],[1869])).
% fof(1871, plain,![X31]:![X32]:![X33]:![X34]:((hAPP(X31,hAPP(c_Hilbert__Choice_Oinv__into(X33,X32,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)),X31),X34))=X34|~(c_Set_Oimage(X33,X32,X31,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X32,tc_HOL_Obool))))&(~(hAPP(X31,hAPP(c_Hilbert__Choice_Oinv__into(X33,X32,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)),X31),esk42_3(X31,X32,X33)))=esk42_3(X31,X32,X33))|c_Set_Oimage(X33,X32,X31,c_Orderings_Otop__class_Otop(tc_fun(X33,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X32,tc_HOL_Obool)))),inference(shift_quantors,[status(thm)],[1870])).
% cnf(1872,plain,(c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),esk42_3(X3,X2,X1)))!=esk42_3(X3,X2,X1)),inference(split_conjunct,[status(thm)],[1871])).
% fof(1903, plain,![X70]:![X71]:hAPP(c_COMBI(X71),X70)=X70,inference(variable_rename,[status(thm)],[356])).
% cnf(1904,plain,(hAPP(c_COMBI(X1),X2)=X2),inference(split_conjunct,[status(thm)],[1903])).
% fof(1913, plain,![X55]:![X21]:![X3]:![X11]:(~(class_Orderings_Oord(X11))|((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X11),X21),X55)))|![X30]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X11,hAPP(X21,X30)),hAPP(X55,X30))))&(?[X30]:~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X11,hAPP(X21,X30)),hAPP(X55,X30))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,X11),X21),X55))))),inference(fof_nnf,[status(thm)],[360])).
% fof(1914, plain,![X56]:![X57]:![X58]:![X59]:(~(class_Orderings_Oord(X59))|((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X58,X59),X57),X56)))|![X60]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X59,hAPP(X57,X60)),hAPP(X56,X60))))&(?[X61]:~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X59,hAPP(X57,X61)),hAPP(X56,X61))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X58,X59),X57),X56))))),inference(variable_rename,[status(thm)],[1913])).
% fof(1915, plain,![X56]:![X57]:![X58]:![X59]:(~(class_Orderings_Oord(X59))|((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X58,X59),X57),X56)))|![X60]:hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X59,hAPP(X57,X60)),hAPP(X56,X60))))&(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X59,hAPP(X57,esk43_4(X56,X57,X58,X59))),hAPP(X56,esk43_4(X56,X57,X58,X59)))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X58,X59),X57),X56))))),inference(skolemize,[status(esa)],[1914])).
% fof(1916, plain,![X56]:![X57]:![X58]:![X59]:![X60]:(((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X59,hAPP(X57,X60)),hAPP(X56,X60)))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X58,X59),X57),X56))))&(~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X59,hAPP(X57,esk43_4(X56,X57,X58,X59))),hAPP(X56,esk43_4(X56,X57,X58,X59)))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X58,X59),X57),X56))))|~(class_Orderings_Oord(X59))),inference(shift_quantors,[status(thm)],[1915])).
% fof(1917, plain,![X56]:![X57]:![X58]:![X59]:![X60]:(((hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X59,hAPP(X57,X60)),hAPP(X56,X60)))|~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X58,X59),X57),X56))))|~(class_Orderings_Oord(X59)))&((~(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X59,hAPP(X57,esk43_4(X56,X57,X58,X59))),hAPP(X56,esk43_4(X56,X57,X58,X59)))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X58,X59),X57),X56)))|~(class_Orderings_Oord(X59)))),inference(distribute,[status(thm)],[1916])).
% cnf(1918,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,esk43_4(X4,X3,X2,X1))),hAPP(X4,esk43_4(X4,X3,X2,X1))))),inference(split_conjunct,[status(thm)],[1917])).
% cnf(1919,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5)),hAPP(X4,X5)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3),X4))),inference(split_conjunct,[status(thm)],[1917])).
% fof(2030, plain,![X23]:hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23)=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X23)),inference(variable_rename,[status(thm)],[393])).
% cnf(2031,plain,(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)=c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1))),inference(split_conjunct,[status(thm)],[2030])).
% cnf(2099,plain,(c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)),inference(split_conjunct,[status(thm)],[414])).
% fof(2214, plain,![X1]:![X21]:![X11]:![X14]:![X3]:(~(hBOOL(hAPP(hAPP(c_member(X3),X14),c_Set_Oimage(X11,X3,X21,X1))))|hAPP(X21,hAPP(c_Hilbert__Choice_Oinv__into(X11,X3,X1,X21),X14))=X14),inference(fof_nnf,[status(thm)],[450])).
% fof(2215, plain,![X22]:![X23]:![X24]:![X25]:![X26]:(~(hBOOL(hAPP(hAPP(c_member(X26),X25),c_Set_Oimage(X24,X26,X23,X22))))|hAPP(X23,hAPP(c_Hilbert__Choice_Oinv__into(X24,X26,X22,X23),X25))=X25),inference(variable_rename,[status(thm)],[2214])).
% cnf(2216,plain,(hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,X4,X1),X5))=X5|~hBOOL(hAPP(hAPP(c_member(X3),X5),c_Set_Oimage(X2,X3,X1,X4)))),inference(split_conjunct,[status(thm)],[2215])).
% cnf(2250,plain,(c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),inference(split_conjunct,[status(thm)],[458])).
% cnf(2502,plain,(hBOOL(hAPP(hAPP(c_fequal,X1),X1))),inference(er,[status(thm)],[938,theory(equality)])).
% cnf(2778,plain,(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),inference(spm,[status(thm)],[2031,2250,theory(equality)])).
% cnf(3829,plain,(hBOOL(hAPP(hAPP(c_member(X1),X3),c_Set_Oimage(X4,X1,c_COMBI(X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))),inference(spm,[status(thm)],[1228,1904,theory(equality)])).
% cnf(4251,plain,(hAPP(c_COMBS(X1,X2,X3,X4,c_COMBI(X5)),X6)=hAPP(hAPP(X4,X6),X6)),inference(spm,[status(thm)],[1080,1904,theory(equality)])).
% cnf(4625,plain,(~c_Finite__Set_Ofinite(tc_Nat_Onat,X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk16_1(X1)),X1))),inference(spm,[status(thm)],[617,902,theory(equality)])).
% cnf(4749,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),inference(spm,[status(thm)],[1315,1312,theory(equality)])).
% cnf(8991,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X2)))|~class_Orderings_Oord(tc_HOL_Obool)),inference(spm,[status(thm)],[1919,1312,theory(equality)])).
% cnf(9000,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X2)))|$false),inference(rw,[status(thm)],[8991,1590,theory(equality)])).
% cnf(9001,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X2)))),inference(cn,[status(thm)],[9000,theory(equality)])).
% cnf(25295,plain,(c_Finite__Set_Ofinite(X1,X2)|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X1,X2)))),inference(rw,[status(thm)],[1614,2778,theory(equality)])).
% cnf(25744,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),inference(spm,[status(thm)],[25295,2099,theory(equality)])).
% cnf(25752,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))|$false),inference(rw,[status(thm)],[25744,1150,theory(equality)])).
% cnf(25753,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))),inference(cn,[status(thm)],[25752,theory(equality)])).
% cnf(29358,plain,(c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1)),inference(spm,[status(thm)],[4749,25753,theory(equality)])).
% cnf(32399,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))|~class_Orderings_Oord(tc_HOL_Obool)),inference(spm,[status(thm)],[1918,9001,theory(equality)])).
% cnf(32468,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))|$false),inference(rw,[status(thm)],[32399,1590,theory(equality)])).
% cnf(32469,plain,(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),inference(cn,[status(thm)],[32468,theory(equality)])).
% cnf(58948,plain,(hAPP(c_COMBI(X1),hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_COMBI(X1)),X4))=X4),inference(spm,[status(thm)],[2216,3829,theory(equality)])).
% cnf(58971,plain,(hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_COMBI(X1)),X4)=X4),inference(rw,[status(thm)],[58948,1904,theory(equality)])).
% cnf(88790,plain,(c_Set_Oimage(X1,X2,c_COMBI(X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(c_COMBI(X3),esk42_3(c_COMBI(X3),X2,X1))!=esk42_3(c_COMBI(X3),X2,X1)),inference(spm,[status(thm)],[1872,58971,theory(equality)])).
% cnf(88824,plain,(c_Set_Oimage(X1,X2,c_COMBI(X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|$false),inference(rw,[status(thm)],[88790,1904,theory(equality)])).
% cnf(88825,plain,(c_Set_Oimage(X1,X2,c_COMBI(X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),inference(cn,[status(thm)],[88824,theory(equality)])).
% cnf(91554,plain,(hBOOL(hAPP(c_COMBS(X2,X3,X4,c_fequal,c_COMBI(X5)),X1))),inference(spm,[status(thm)],[2502,4251,theory(equality)])).
% cnf(156615,plain,(~c_Finite__Set_Ofinite(tc_Nat_Onat,X1)|~hBOOL(hAPP(X1,esk16_1(X1)))),inference(spm,[status(thm)],[4625,608,theory(equality)])).
% cnf(158073,plain,(~c_Finite__Set_Ofinite(tc_Nat_Onat,c_COMBS(X1,X2,X3,c_fequal,c_COMBI(X4)))),inference(spm,[status(thm)],[156615,91554,theory(equality)])).
% cnf(244396,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X3,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))|~hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),inference(spm,[status(thm)],[1575,88825,theory(equality)])).
% cnf(244458,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X3,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))|$false),inference(rw,[status(thm)],[244396,32469,theory(equality)])).
% cnf(244459,plain,(c_Finite__Set_Ofinite(X1,X2)|~c_Finite__Set_Ofinite(X3,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),inference(cn,[status(thm)],[244458,theory(equality)])).
% cnf(244494,plain,(c_Finite__Set_Ofinite(X1,X2)),inference(spm,[status(thm)],[244459,29358,theory(equality)])).
% cnf(244721,plain,($false),inference(rw,[status(thm)],[158073,244494,theory(equality)])).
% cnf(244722,plain,($false),inference(cn,[status(thm)],[244721,theory(equality)])).
% cnf(244723,plain,($false),244722,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 9023
% # ...of these trivial : 317
% # ...subsumed : 6107
% # ...remaining for further processing: 2599
% # Other redundant clauses eliminated : 898
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 33
% # Backward-rewritten : 265
% # Generated clauses : 175380
% # ...of the previous two non-trivial : 159486
% # Contextual simplify-reflections : 696
% # Paramodulations : 174394
% # Factorizations : 17
% # Equation resolutions : 975
% # Current number of processed clauses: 1662
% # Positive orientable unit clauses: 451
% # Positive unorientable unit clauses: 36
% # Negative unit clauses : 116
% # Non-unit-clauses : 1059
% # Current number of unprocessed clauses: 136743
% # ...number of literals in the above : 434499
% # Clause-clause subsumption calls (NU) : 219052
% # Rec. Clause-clause subsumption calls : 167823
% # Unit Clause-clause subsumption calls : 11242
% # Rewrite failures with RHS unbound : 421
% # Indexed BW rewrite attempts : 15855
% # Indexed BW rewrite successes : 358
% # Backwards rewriting index: 1324 leaves, 2.80+/-8.103 terms/leaf
% # Paramod-from index: 325 leaves, 2.57+/-7.195 terms/leaf
% # Paramod-into index: 1197 leaves, 2.56+/-6.777 terms/leaf
% # -------------------------------------------------
% # User time : 8.793 s
% # System time : 0.290 s
% # Total time : 9.083 s
% # Maximum resident set size: 0 pages
% PrfWatch: 13.48 CPU 13.65 WC
% FINAL PrfWatch: 13.48 CPU 13.65 WC
% SZS output end Solution for /tmp/SystemOnTPTP13847/SCT168+1.tptp
%
%------------------------------------------------------------------------------