TSTP Solution File: SCT122+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SCT122+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 : art01.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 : Sun Mar 6 23:51:05 EST 2011
% Result : Theorem 62.53s
% Output : Solution 62.53s
% 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/SystemOnTPTP9730/SCT122+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP9730/SCT122+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP9730/SCT122+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 9854
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.01 WC
% PrfWatch: 1.94 CPU 2.02 WC
% PrfWatch: 3.93 CPU 4.03 WC
% PrfWatch: 5.92 CPU 6.04 WC
% PrfWatch: 7.91 CPU 8.04 WC
% PrfWatch: 9.90 CPU 10.05 WC
% PrfWatch: 11.89 CPU 12.06 WC
% PrfWatch: 13.87 CPU 14.06 WC
% PrfWatch: 15.86 CPU 16.07 WC
% PrfWatch: 17.85 CPU 18.08 WC
% PrfWatch: 19.83 CPU 20.08 WC
% PrfWatch: 21.82 CPU 22.09 WC
% PrfWatch: 23.81 CPU 24.10 WC
% PrfWatch: 25.80 CPU 26.11 WC
% PrfWatch: 27.78 CPU 28.11 WC
% PrfWatch: 29.77 CPU 30.12 WC
% PrfWatch: 31.74 CPU 32.13 WC
% PrfWatch: 33.73 CPU 34.13 WC
% # Preprocessing time : 0.113 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 35.70 CPU 36.14 WC
% PrfWatch: 37.68 CPU 38.15 WC
% PrfWatch: 39.39 CPU 40.16 WC
% PrfWatch: 41.15 CPU 42.16 WC
% PrfWatch: 43.14 CPU 44.17 WC
% PrfWatch: 45.13 CPU 46.18 WC
% PrfWatch: 47.13 CPU 48.18 WC
% # SZS output start CNFRefutation.
% fof(3, axiom,![X6]:![X5]:(c_Relation_Oirrefl(X5,X6)<=>![X3]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6))),file('/tmp/SRASS.s.p', fact_irrefl__def)).
% fof(4, axiom,![X6]:![X7]:![X5]:(c_Relation_Ototal__on(X5,X7,X6)<=>![X3]:(c_member(X5,X3,X7)=>![X8]:(c_member(X5,X8,X7)=>(~(X3=X8)=>(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X8),X6)|c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X8,X3),X6)))))),file('/tmp/SRASS.s.p', fact_total__on__def)).
% fof(15, axiom,![X3]:((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3))),file('/tmp/SRASS.s.p', conj_0)).
% fof(16, axiom,c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),file('/tmp/SRASS.s.p', conj_1)).
% fof(17, axiom,(![X3]:((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3)))=>((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)))),file('/tmp/SRASS.s.p', conj_2)).
% fof(18, axiom,(![X3]:((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3)))=>![X23]:![X24]:(~(X23=X24)=>(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X23,X24),hAPP(v_P,v_i))=>c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X23,X24),v_F(v_P))))),file('/tmp/SRASS.s.p', conj_3)).
% fof(32, axiom,![X4]:![X5]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X4)),file('/tmp/SRASS.s.p', fact_top1I)).
% fof(37, axiom,![X7]:![X5]:c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))=X7,file('/tmp/SRASS.s.p', fact_Int__UNIV__right)).
% fof(52, axiom,![X6]:![X5]:(c_Relation_Oantisym(X5,X6)<=>![X3]:![X9]:(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X9),X6)=>(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X3),X6)=>X3=X9))),file('/tmp/SRASS.s.p', fact_antisym__def)).
% fof(58, axiom,![X7]:![X5]:c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),file('/tmp/SRASS.s.p', fact_subset__UNIV)).
% fof(86, axiom,![X15]:![X4]:![X30]:![X20]:![X5]:(c_FunDef_Oin__rel(X5,X20,X30,X4,X15)<=>c_member(tc_prod(X5,X20),c_Product__Type_OPair(X5,X20,X4,X15),X30)),file('/tmp/SRASS.s.p', fact_in__rel__def)).
% fof(141, axiom,![X7]:![X4]:![X5]:(c_member(X5,X4,X7)<=>hBOOL(hAPP(X7,X4))),file('/tmp/SRASS.s.p', fact_mem__def)).
% fof(149, axiom,![X6]:![X5]:(c_Relation_Otrans(X5,X6)=>c_Transitive__Closure_Otrancl(X5,X6)=X6),file('/tmp/SRASS.s.p', fact_trancl__id)).
% fof(217, axiom,![X6]:![X5]:(c_Wellfounded_Oacyclic(X5,X6)<=>![X3]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6)))),file('/tmp/SRASS.s.p', fact_acyclic__def)).
% fof(277, axiom,![X5]:c_Transitive__Closure_Ortrancl(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)))=c_Relation_OId(X5),file('/tmp/SRASS.s.p', fact_rtrancl__empty)).
% fof(282, axiom,![X1]:![X2]:![X5]:![X20]:(class_Orderings_Oord(X20)=>(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20),X2,X1)<=>![X3]:c_Orderings_Oord__class_Oless__eq(X20,hAPP(X2,X3),hAPP(X1,X3)))),file('/tmp/SRASS.s.p', fact_le__fun__def)).
% fof(298, axiom,![X6]:![X5]:(c_Relation_Oantisym(X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X6,c_Relation_OId(X5)))<=>c_Relation_Oantisym(X5,X6)),file('/tmp/SRASS.s.p', fact_antisym__reflcl)).
% fof(315, axiom,![X7]:![X14]:![X5]:(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X14,X7)=>c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X14)=X14),file('/tmp/SRASS.s.p', fact_Int__absorb1)).
% fof(366, axiom,![X6]:![X5]:c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X5,X6),c_Relation_OId(X5))=c_Transitive__Closure_Ortrancl(X5,X6),file('/tmp/SRASS.s.p', fact_reflcl__trancl)).
% fof(377, axiom,class_Orderings_Oord(tc_HOL_Obool),file('/tmp/SRASS.s.p', arity_HOL__Obool__Orderings_Oord)).
% fof(381, axiom,![X6]:![X5]:(c_Wellfounded_Oacyclic(X5,X6)=>c_Relation_Oantisym(X5,c_Transitive__Closure_Ortrancl(X5,X6))),file('/tmp/SRASS.s.p', fact_acyclic__impl__antisym__rtrancl)).
% fof(406, axiom,![X30]:![X5]:c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Otrancl(X5,X30))=c_Transitive__Closure_Ortrancl(X5,X30),file('/tmp/SRASS.s.p', fact_trancl__rtrancl__absorb)).
% fof(527, conjecture,c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),file('/tmp/SRASS.s.p', conj_4)).
% fof(528, negated_conjecture,~(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i))),inference(assume_negation,[status(cth)],[527])).
% fof(529, plain,![X6]:![X5]:(c_Relation_Oirrefl(X5,X6)<=>![X3]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6))),inference(fof_simplification,[status(thm)],[3,theory(equality)])).
% fof(568, plain,![X6]:![X5]:(c_Wellfounded_Oacyclic(X5,X6)<=>![X3]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6)))),inference(fof_simplification,[status(thm)],[217,theory(equality)])).
% fof(580, negated_conjecture,~(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i))),inference(fof_simplification,[status(thm)],[528,theory(equality)])).
% fof(587, plain,![X6]:![X5]:((~(c_Relation_Oirrefl(X5,X6))|![X3]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6)))&(?[X3]:c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6)|c_Relation_Oirrefl(X5,X6))),inference(fof_nnf,[status(thm)],[529])).
% fof(588, plain,![X7]:![X8]:((~(c_Relation_Oirrefl(X8,X7))|![X9]:~(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,X9,X9),X7)))&(?[X10]:c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,X10,X10),X7)|c_Relation_Oirrefl(X8,X7))),inference(variable_rename,[status(thm)],[587])).
% fof(589, plain,![X7]:![X8]:((~(c_Relation_Oirrefl(X8,X7))|![X9]:~(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,X9,X9),X7)))&(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,esk2_2(X7,X8),esk2_2(X7,X8)),X7)|c_Relation_Oirrefl(X8,X7))),inference(skolemize,[status(esa)],[588])).
% fof(590, plain,![X7]:![X8]:![X9]:((~(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,X9,X9),X7))|~(c_Relation_Oirrefl(X8,X7)))&(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,esk2_2(X7,X8),esk2_2(X7,X8)),X7)|c_Relation_Oirrefl(X8,X7))),inference(shift_quantors,[status(thm)],[589])).
% cnf(592,plain,(~c_Relation_Oirrefl(X1,X2)|~c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),X2)),inference(split_conjunct,[status(thm)],[590])).
% fof(593, plain,![X6]:![X7]:![X5]:((~(c_Relation_Ototal__on(X5,X7,X6))|![X3]:(~(c_member(X5,X3,X7))|![X8]:(~(c_member(X5,X8,X7))|(X3=X8|(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X8),X6)|c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X8,X3),X6))))))&(?[X3]:(c_member(X5,X3,X7)&?[X8]:(c_member(X5,X8,X7)&(~(X3=X8)&(~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X8),X6))&~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X8,X3),X6))))))|c_Relation_Ototal__on(X5,X7,X6))),inference(fof_nnf,[status(thm)],[4])).
% fof(594, plain,![X9]:![X10]:![X11]:((~(c_Relation_Ototal__on(X11,X10,X9))|![X12]:(~(c_member(X11,X12,X10))|![X13]:(~(c_member(X11,X13,X10))|(X12=X13|(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X12,X13),X9)|c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X13,X12),X9))))))&(?[X14]:(c_member(X11,X14,X10)&?[X15]:(c_member(X11,X15,X10)&(~(X14=X15)&(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X14,X15),X9))&~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X15,X14),X9))))))|c_Relation_Ototal__on(X11,X10,X9))),inference(variable_rename,[status(thm)],[593])).
% fof(595, plain,![X9]:![X10]:![X11]:((~(c_Relation_Ototal__on(X11,X10,X9))|![X12]:(~(c_member(X11,X12,X10))|![X13]:(~(c_member(X11,X13,X10))|(X12=X13|(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X12,X13),X9)|c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X13,X12),X9))))))&((c_member(X11,esk3_3(X9,X10,X11),X10)&(c_member(X11,esk4_3(X9,X10,X11),X10)&(~(esk3_3(X9,X10,X11)=esk4_3(X9,X10,X11))&(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk3_3(X9,X10,X11),esk4_3(X9,X10,X11)),X9))&~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk4_3(X9,X10,X11),esk3_3(X9,X10,X11)),X9))))))|c_Relation_Ototal__on(X11,X10,X9))),inference(skolemize,[status(esa)],[594])).
% fof(596, plain,![X9]:![X10]:![X11]:![X12]:![X13]:((((~(c_member(X11,X13,X10))|(X12=X13|(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X12,X13),X9)|c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X13,X12),X9))))|~(c_member(X11,X12,X10)))|~(c_Relation_Ototal__on(X11,X10,X9)))&((c_member(X11,esk3_3(X9,X10,X11),X10)&(c_member(X11,esk4_3(X9,X10,X11),X10)&(~(esk3_3(X9,X10,X11)=esk4_3(X9,X10,X11))&(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk3_3(X9,X10,X11),esk4_3(X9,X10,X11)),X9))&~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk4_3(X9,X10,X11),esk3_3(X9,X10,X11)),X9))))))|c_Relation_Ototal__on(X11,X10,X9))),inference(shift_quantors,[status(thm)],[595])).
% fof(597, plain,![X9]:![X10]:![X11]:![X12]:![X13]:((((~(c_member(X11,X13,X10))|(X12=X13|(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X12,X13),X9)|c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X13,X12),X9))))|~(c_member(X11,X12,X10)))|~(c_Relation_Ototal__on(X11,X10,X9)))&((c_member(X11,esk3_3(X9,X10,X11),X10)|c_Relation_Ototal__on(X11,X10,X9))&((c_member(X11,esk4_3(X9,X10,X11),X10)|c_Relation_Ototal__on(X11,X10,X9))&((~(esk3_3(X9,X10,X11)=esk4_3(X9,X10,X11))|c_Relation_Ototal__on(X11,X10,X9))&((~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk3_3(X9,X10,X11),esk4_3(X9,X10,X11)),X9))|c_Relation_Ototal__on(X11,X10,X9))&(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk4_3(X9,X10,X11),esk3_3(X9,X10,X11)),X9))|c_Relation_Ototal__on(X11,X10,X9))))))),inference(distribute,[status(thm)],[596])).
% cnf(603,plain,(c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X3)|c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X3)|X4=X5|~c_Relation_Ototal__on(X1,X2,X3)|~c_member(X1,X4,X2)|~c_member(X1,X5,X2)),inference(split_conjunct,[status(thm)],[597])).
% fof(656, plain,![X4]:((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X4))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X4)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X4))),inference(variable_rename,[status(thm)],[15])).
% cnf(657,plain,(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X1))),inference(split_conjunct,[status(thm)],[656])).
% cnf(658,plain,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1))),inference(split_conjunct,[status(thm)],[656])).
% cnf(659,plain,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1))),inference(split_conjunct,[status(thm)],[656])).
% cnf(660,plain,(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P))),inference(split_conjunct,[status(thm)],[16])).
% fof(661, plain,(?[X3]:((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3))))|((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)))),inference(fof_nnf,[status(thm)],[17])).
% fof(662, plain,(?[X4]:((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X4)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X4))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X4))))|((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)))),inference(variable_rename,[status(thm)],[661])).
% fof(663, plain,(((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0))))|((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))&c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)))),inference(skolemize,[status(esa)],[662])).
% fof(664, plain,(((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0)))))&(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0))))))&(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P))|((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0)))))),inference(distribute,[status(thm)],[663])).
% cnf(666,plain,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))),inference(split_conjunct,[status(thm)],[664])).
% cnf(667,plain,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))),inference(split_conjunct,[status(thm)],[664])).
% fof(668, plain,(?[X3]:((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3))))|![X23]:![X24]:(X23=X24|(~(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X23,X24),hAPP(v_P,v_i)))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X23,X24),v_F(v_P))))),inference(fof_nnf,[status(thm)],[18])).
% fof(669, plain,(?[X25]:((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X25)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X25))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X25))))|![X26]:![X27]:(X26=X27|(~(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X26,X27),hAPP(v_P,v_i)))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X26,X27),v_F(v_P))))),inference(variable_rename,[status(thm)],[668])).
% fof(670, plain,(((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk12_0)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk12_0))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk12_0))))|![X26]:![X27]:(X26=X27|(~(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X26,X27),hAPP(v_P,v_i)))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X26,X27),v_F(v_P))))),inference(skolemize,[status(esa)],[669])).
% fof(671, plain,![X26]:![X27]:((X26=X27|(~(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X26,X27),hAPP(v_P,v_i)))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X26,X27),v_F(v_P))))|((~(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk12_0)))|~(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk12_0))))|~(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk12_0))))),inference(shift_quantors,[status(thm)],[670])).
% cnf(672,plain,(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))|X1=X2|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk12_0))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk12_0))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk12_0))|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i))),inference(split_conjunct,[status(thm)],[671])).
% fof(743, plain,![X6]:![X7]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),X6)),inference(variable_rename,[status(thm)],[32])).
% cnf(744,plain,(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2))),inference(split_conjunct,[status(thm)],[743])).
% fof(764, plain,![X8]:![X9]:c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9,tc_HOL_Obool),X8,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))=X8,inference(variable_rename,[status(thm)],[37])).
% cnf(765,plain,(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=X2),inference(split_conjunct,[status(thm)],[764])).
% fof(836, plain,![X6]:![X5]:((~(c_Relation_Oantisym(X5,X6))|![X3]:![X9]:(~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X9),X6))|(~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X3),X6))|X3=X9)))&(?[X3]:?[X9]:(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X9),X6)&(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X3),X6)&~(X3=X9)))|c_Relation_Oantisym(X5,X6))),inference(fof_nnf,[status(thm)],[52])).
% fof(837, plain,![X10]:![X11]:((~(c_Relation_Oantisym(X11,X10))|![X12]:![X13]:(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X12,X13),X10))|(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X13,X12),X10))|X12=X13)))&(?[X14]:?[X15]:(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X14,X15),X10)&(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X15,X14),X10)&~(X14=X15)))|c_Relation_Oantisym(X11,X10))),inference(variable_rename,[status(thm)],[836])).
% fof(838, plain,![X10]:![X11]:((~(c_Relation_Oantisym(X11,X10))|![X12]:![X13]:(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X12,X13),X10))|(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X13,X12),X10))|X12=X13)))&((c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk33_2(X10,X11),esk34_2(X10,X11)),X10)&(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk34_2(X10,X11),esk33_2(X10,X11)),X10)&~(esk33_2(X10,X11)=esk34_2(X10,X11))))|c_Relation_Oantisym(X11,X10))),inference(skolemize,[status(esa)],[837])).
% fof(839, plain,![X10]:![X11]:![X12]:![X13]:(((~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X12,X13),X10))|(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X13,X12),X10))|X12=X13))|~(c_Relation_Oantisym(X11,X10)))&((c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk33_2(X10,X11),esk34_2(X10,X11)),X10)&(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk34_2(X10,X11),esk33_2(X10,X11)),X10)&~(esk33_2(X10,X11)=esk34_2(X10,X11))))|c_Relation_Oantisym(X11,X10))),inference(shift_quantors,[status(thm)],[838])).
% fof(840, plain,![X10]:![X11]:![X12]:![X13]:(((~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X12,X13),X10))|(~(c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,X13,X12),X10))|X12=X13))|~(c_Relation_Oantisym(X11,X10)))&((c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk33_2(X10,X11),esk34_2(X10,X11)),X10)|c_Relation_Oantisym(X11,X10))&((c_member(tc_prod(X11,X11),c_Product__Type_OPair(X11,X11,esk34_2(X10,X11),esk33_2(X10,X11)),X10)|c_Relation_Oantisym(X11,X10))&(~(esk33_2(X10,X11)=esk34_2(X10,X11))|c_Relation_Oantisym(X11,X10))))),inference(distribute,[status(thm)],[839])).
% cnf(844,plain,(X3=X4|~c_Relation_Oantisym(X1,X2)|~c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X3),X2)|~c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X4),X2)),inference(split_conjunct,[status(thm)],[840])).
% fof(874, plain,![X8]:![X9]:c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X8,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))),inference(variable_rename,[status(thm)],[58])).
% cnf(875,plain,(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)],[874])).
% fof(1006, plain,![X15]:![X4]:![X30]:![X20]:![X5]:((~(c_FunDef_Oin__rel(X5,X20,X30,X4,X15))|c_member(tc_prod(X5,X20),c_Product__Type_OPair(X5,X20,X4,X15),X30))&(~(c_member(tc_prod(X5,X20),c_Product__Type_OPair(X5,X20,X4,X15),X30))|c_FunDef_Oin__rel(X5,X20,X30,X4,X15))),inference(fof_nnf,[status(thm)],[86])).
% fof(1007, plain,![X31]:![X32]:![X33]:![X34]:![X35]:((~(c_FunDef_Oin__rel(X35,X34,X33,X32,X31))|c_member(tc_prod(X35,X34),c_Product__Type_OPair(X35,X34,X32,X31),X33))&(~(c_member(tc_prod(X35,X34),c_Product__Type_OPair(X35,X34,X32,X31),X33))|c_FunDef_Oin__rel(X35,X34,X33,X32,X31))),inference(variable_rename,[status(thm)],[1006])).
% cnf(1008,plain,(c_FunDef_Oin__rel(X1,X2,X3,X4,X5)|~c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X4,X5),X3)),inference(split_conjunct,[status(thm)],[1007])).
% cnf(1009,plain,(c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X3,X4),X5)|~c_FunDef_Oin__rel(X1,X2,X5,X3,X4)),inference(split_conjunct,[status(thm)],[1007])).
% fof(1209, plain,![X7]:![X4]:![X5]:((~(c_member(X5,X4,X7))|hBOOL(hAPP(X7,X4)))&(~(hBOOL(hAPP(X7,X4)))|c_member(X5,X4,X7))),inference(fof_nnf,[status(thm)],[141])).
% fof(1210, plain,![X8]:![X9]:![X10]:((~(c_member(X10,X9,X8))|hBOOL(hAPP(X8,X9)))&(~(hBOOL(hAPP(X8,X9)))|c_member(X10,X9,X8))),inference(variable_rename,[status(thm)],[1209])).
% cnf(1211,plain,(c_member(X1,X2,X3)|~hBOOL(hAPP(X3,X2))),inference(split_conjunct,[status(thm)],[1210])).
% cnf(1212,plain,(hBOOL(hAPP(X1,X2))|~c_member(X3,X2,X1)),inference(split_conjunct,[status(thm)],[1210])).
% fof(1253, plain,![X6]:![X5]:(~(c_Relation_Otrans(X5,X6))|c_Transitive__Closure_Otrancl(X5,X6)=X6),inference(fof_nnf,[status(thm)],[149])).
% fof(1254, plain,![X7]:![X8]:(~(c_Relation_Otrans(X8,X7))|c_Transitive__Closure_Otrancl(X8,X7)=X7),inference(variable_rename,[status(thm)],[1253])).
% cnf(1255,plain,(c_Transitive__Closure_Otrancl(X1,X2)=X2|~c_Relation_Otrans(X1,X2)),inference(split_conjunct,[status(thm)],[1254])).
% fof(1499, plain,![X6]:![X5]:((~(c_Wellfounded_Oacyclic(X5,X6))|![X3]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6))))&(?[X3]:c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6))|c_Wellfounded_Oacyclic(X5,X6))),inference(fof_nnf,[status(thm)],[568])).
% fof(1500, plain,![X7]:![X8]:((~(c_Wellfounded_Oacyclic(X8,X7))|![X9]:~(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,X9,X9),c_Transitive__Closure_Otrancl(X8,X7))))&(?[X10]:c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,X10,X10),c_Transitive__Closure_Otrancl(X8,X7))|c_Wellfounded_Oacyclic(X8,X7))),inference(variable_rename,[status(thm)],[1499])).
% fof(1501, plain,![X7]:![X8]:((~(c_Wellfounded_Oacyclic(X8,X7))|![X9]:~(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,X9,X9),c_Transitive__Closure_Otrancl(X8,X7))))&(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,esk80_2(X7,X8),esk80_2(X7,X8)),c_Transitive__Closure_Otrancl(X8,X7))|c_Wellfounded_Oacyclic(X8,X7))),inference(skolemize,[status(esa)],[1500])).
% fof(1502, plain,![X7]:![X8]:![X9]:((~(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,X9,X9),c_Transitive__Closure_Otrancl(X8,X7)))|~(c_Wellfounded_Oacyclic(X8,X7)))&(c_member(tc_prod(X8,X8),c_Product__Type_OPair(X8,X8,esk80_2(X7,X8),esk80_2(X7,X8)),c_Transitive__Closure_Otrancl(X8,X7))|c_Wellfounded_Oacyclic(X8,X7))),inference(shift_quantors,[status(thm)],[1501])).
% cnf(1503,plain,(c_Wellfounded_Oacyclic(X1,X2)|c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,esk80_2(X2,X1),esk80_2(X2,X1)),c_Transitive__Closure_Otrancl(X1,X2))),inference(split_conjunct,[status(thm)],[1502])).
% cnf(1504,plain,(~c_Wellfounded_Oacyclic(X1,X2)|~c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X2))),inference(split_conjunct,[status(thm)],[1502])).
% fof(1695, plain,![X6]:c_Transitive__Closure_Ortrancl(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)))=c_Relation_OId(X6),inference(variable_rename,[status(thm)],[277])).
% cnf(1696,plain,(c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=c_Relation_OId(X1)),inference(split_conjunct,[status(thm)],[1695])).
% fof(1711, plain,![X1]:![X2]:![X5]:![X20]:(~(class_Orderings_Oord(X20))|((~(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20),X2,X1))|![X3]:c_Orderings_Oord__class_Oless__eq(X20,hAPP(X2,X3),hAPP(X1,X3)))&(?[X3]:~(c_Orderings_Oord__class_Oless__eq(X20,hAPP(X2,X3),hAPP(X1,X3)))|c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20),X2,X1)))),inference(fof_nnf,[status(thm)],[282])).
% fof(1712, plain,![X21]:![X22]:![X23]:![X24]:(~(class_Orderings_Oord(X24))|((~(c_Orderings_Oord__class_Oless__eq(tc_fun(X23,X24),X22,X21))|![X25]:c_Orderings_Oord__class_Oless__eq(X24,hAPP(X22,X25),hAPP(X21,X25)))&(?[X26]:~(c_Orderings_Oord__class_Oless__eq(X24,hAPP(X22,X26),hAPP(X21,X26)))|c_Orderings_Oord__class_Oless__eq(tc_fun(X23,X24),X22,X21)))),inference(variable_rename,[status(thm)],[1711])).
% fof(1713, plain,![X21]:![X22]:![X23]:![X24]:(~(class_Orderings_Oord(X24))|((~(c_Orderings_Oord__class_Oless__eq(tc_fun(X23,X24),X22,X21))|![X25]:c_Orderings_Oord__class_Oless__eq(X24,hAPP(X22,X25),hAPP(X21,X25)))&(~(c_Orderings_Oord__class_Oless__eq(X24,hAPP(X22,esk86_4(X21,X22,X23,X24)),hAPP(X21,esk86_4(X21,X22,X23,X24))))|c_Orderings_Oord__class_Oless__eq(tc_fun(X23,X24),X22,X21)))),inference(skolemize,[status(esa)],[1712])).
% fof(1714, plain,![X21]:![X22]:![X23]:![X24]:![X25]:(((c_Orderings_Oord__class_Oless__eq(X24,hAPP(X22,X25),hAPP(X21,X25))|~(c_Orderings_Oord__class_Oless__eq(tc_fun(X23,X24),X22,X21)))&(~(c_Orderings_Oord__class_Oless__eq(X24,hAPP(X22,esk86_4(X21,X22,X23,X24)),hAPP(X21,esk86_4(X21,X22,X23,X24))))|c_Orderings_Oord__class_Oless__eq(tc_fun(X23,X24),X22,X21)))|~(class_Orderings_Oord(X24))),inference(shift_quantors,[status(thm)],[1713])).
% fof(1715, plain,![X21]:![X22]:![X23]:![X24]:![X25]:(((c_Orderings_Oord__class_Oless__eq(X24,hAPP(X22,X25),hAPP(X21,X25))|~(c_Orderings_Oord__class_Oless__eq(tc_fun(X23,X24),X22,X21)))|~(class_Orderings_Oord(X24)))&((~(c_Orderings_Oord__class_Oless__eq(X24,hAPP(X22,esk86_4(X21,X22,X23,X24)),hAPP(X21,esk86_4(X21,X22,X23,X24))))|c_Orderings_Oord__class_Oless__eq(tc_fun(X23,X24),X22,X21))|~(class_Orderings_Oord(X24)))),inference(distribute,[status(thm)],[1714])).
% cnf(1716,plain,(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)|~class_Orderings_Oord(X1)|~c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,esk86_4(X4,X3,X2,X1)),hAPP(X4,esk86_4(X4,X3,X2,X1)))),inference(split_conjunct,[status(thm)],[1715])).
% cnf(1717,plain,(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))|~class_Orderings_Oord(X1)|~c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4)),inference(split_conjunct,[status(thm)],[1715])).
% fof(1763, plain,![X6]:![X5]:((~(c_Relation_Oantisym(X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X6,c_Relation_OId(X5))))|c_Relation_Oantisym(X5,X6))&(~(c_Relation_Oantisym(X5,X6))|c_Relation_Oantisym(X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X6,c_Relation_OId(X5))))),inference(fof_nnf,[status(thm)],[298])).
% fof(1764, plain,![X7]:![X8]:((~(c_Relation_Oantisym(X8,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),X7,c_Relation_OId(X8))))|c_Relation_Oantisym(X8,X7))&(~(c_Relation_Oantisym(X8,X7))|c_Relation_Oantisym(X8,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),X7,c_Relation_OId(X8))))),inference(variable_rename,[status(thm)],[1763])).
% cnf(1766,plain,(c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Relation_OId(X1)))),inference(split_conjunct,[status(thm)],[1764])).
% fof(1814, plain,![X7]:![X14]:![X5]:(~(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X14,X7))|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X14)=X14),inference(fof_nnf,[status(thm)],[315])).
% fof(1815, plain,![X15]:![X16]:![X17]:(~(c_Orderings_Oord__class_Oless__eq(tc_fun(X17,tc_HOL_Obool),X16,X15))|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17,tc_HOL_Obool),X15,X16)=X16),inference(variable_rename,[status(thm)],[1814])).
% cnf(1816,plain,(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3)=X3|~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2)),inference(split_conjunct,[status(thm)],[1815])).
% fof(1949, plain,![X7]:![X8]:c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X8,X7),c_Relation_OId(X8))=c_Transitive__Closure_Ortrancl(X8,X7),inference(variable_rename,[status(thm)],[366])).
% cnf(1950,plain,(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X1))=c_Transitive__Closure_Ortrancl(X1,X2)),inference(split_conjunct,[status(thm)],[1949])).
% cnf(1970,plain,(class_Orderings_Oord(tc_HOL_Obool)),inference(split_conjunct,[status(thm)],[377])).
% fof(1984, plain,![X6]:![X5]:(~(c_Wellfounded_Oacyclic(X5,X6))|c_Relation_Oantisym(X5,c_Transitive__Closure_Ortrancl(X5,X6))),inference(fof_nnf,[status(thm)],[381])).
% fof(1985, plain,![X7]:![X8]:(~(c_Wellfounded_Oacyclic(X8,X7))|c_Relation_Oantisym(X8,c_Transitive__Closure_Ortrancl(X8,X7))),inference(variable_rename,[status(thm)],[1984])).
% cnf(1986,plain,(c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))|~c_Wellfounded_Oacyclic(X1,X2)),inference(split_conjunct,[status(thm)],[1985])).
% fof(2057, plain,![X31]:![X32]:c_Transitive__Closure_Ortrancl(X32,c_Transitive__Closure_Otrancl(X32,X31))=c_Transitive__Closure_Ortrancl(X32,X31),inference(variable_rename,[status(thm)],[406])).
% cnf(2058,plain,(c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2)),inference(split_conjunct,[status(thm)],[2057])).
% cnf(2434,negated_conjecture,(~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i))),inference(split_conjunct,[status(thm)],[580])).
% cnf(2448,plain,(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))=c_Transitive__Closure_Ortrancl(X1,X2)),inference(rw,[status(thm)],[1950,1696,theory(equality)]),['unfolding']).
% cnf(2453,plain,(c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(X1,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))),inference(rw,[status(thm)],[1766,1696,theory(equality)]),['unfolding']).
% cnf(2525,plain,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|$false|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0))),inference(rw,[status(thm)],[666,658,theory(equality)])).
% cnf(2526,plain,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|$false|$false|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0))),inference(rw,[status(thm)],[2525,659,theory(equality)])).
% cnf(2527,plain,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|$false|$false|$false),inference(rw,[status(thm)],[2526,657,theory(equality)])).
% cnf(2528,plain,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),inference(cn,[status(thm)],[2527,theory(equality)])).
% cnf(2529,plain,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|$false|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk11_0))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0))),inference(rw,[status(thm)],[667,658,theory(equality)])).
% cnf(2530,plain,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|$false|$false|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk11_0))),inference(rw,[status(thm)],[2529,659,theory(equality)])).
% cnf(2531,plain,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|$false|$false|$false),inference(rw,[status(thm)],[2530,657,theory(equality)])).
% cnf(2532,plain,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),inference(cn,[status(thm)],[2531,theory(equality)])).
% cnf(2576,plain,(X1=X2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))|$false|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk12_0))|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk12_0))|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i))),inference(rw,[status(thm)],[672,658,theory(equality)])).
% cnf(2577,plain,(X1=X2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))|$false|$false|~c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk12_0))|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i))),inference(rw,[status(thm)],[2576,659,theory(equality)])).
% cnf(2578,plain,(X1=X2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))|$false|$false|$false|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i))),inference(rw,[status(thm)],[2577,657,theory(equality)])).
% cnf(2579,plain,(X1=X2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i))),inference(cn,[status(thm)],[2578,theory(equality)])).
% cnf(2600,plain,(c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))=v_F(v_P)),inference(spm,[status(thm)],[1255,2532,theory(equality)])).
% cnf(2608,plain,(hBOOL(hAPP(v_F(v_P),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b)))),inference(spm,[status(thm)],[1212,660,theory(equality)])).
% cnf(2617,plain,(c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),inference(spm,[status(thm)],[1211,744,theory(equality)])).
% cnf(2635,plain,(c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))|~c_Wellfounded_Oacyclic(X1,c_Transitive__Closure_Otrancl(X1,X2))),inference(spm,[status(thm)],[1986,2058,theory(equality)])).
% cnf(3202,plain,(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_b)),inference(spm,[status(thm)],[1008,660,theory(equality)])).
% cnf(3340,plain,(~c_Wellfounded_Oacyclic(X1,X2)|~c_FunDef_Oin__rel(X1,X1,c_Transitive__Closure_Otrancl(X1,X2),X3,X3)),inference(spm,[status(thm)],[1504,1009,theory(equality)])).
% cnf(3665,plain,(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=X2|~c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),inference(spm,[status(thm)],[765,1816,theory(equality)])).
% cnf(6315,plain,(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)],[1717,875,theory(equality)])).
% cnf(6334,plain,(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))|$false),inference(rw,[status(thm)],[6315,1970,theory(equality)])).
% cnf(6335,plain,(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X2))),inference(cn,[status(thm)],[6334,theory(equality)])).
% cnf(8721,plain,(c_Wellfounded_Oacyclic(X1,X2)|~c_Relation_Oirrefl(X1,c_Transitive__Closure_Otrancl(X1,X2))),inference(spm,[status(thm)],[592,1503,theory(equality)])).
% cnf(11952,plain,(c_Relation_Oantisym(X1,c_Transitive__Closure_Otrancl(X1,X2))|~c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))),inference(spm,[status(thm)],[2453,2448,theory(equality)])).
% cnf(23943,plain,(c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P))),inference(spm,[status(thm)],[1211,2608,theory(equality)])).
% cnf(23957,plain,(v_b=v_a|~c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))),inference(spm,[status(thm)],[844,23943,theory(equality)])).
% cnf(24542,plain,(c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))|~c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),inference(spm,[status(thm)],[2635,2600,theory(equality)])).
% cnf(33560,plain,(c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),inference(spm,[status(thm)],[8721,2600,theory(equality)])).
% cnf(33569,plain,(c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|$false),inference(rw,[status(thm)],[33560,2528,theory(equality)])).
% cnf(33570,plain,(c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),inference(cn,[status(thm)],[33569,theory(equality)])).
% cnf(50382,plain,(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)],[1716,6335,theory(equality)])).
% cnf(50428,plain,(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))|$false),inference(rw,[status(thm)],[50382,1970,theory(equality)])).
% cnf(50429,plain,(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),inference(cn,[status(thm)],[50428,theory(equality)])).
% cnf(57935,plain,(~c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),X1,X1)),inference(spm,[status(thm)],[3340,2600,theory(equality)])).
% cnf(57945,plain,($false|~c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),X1,X1)),inference(rw,[status(thm)],[57935,33570,theory(equality)])).
% cnf(57946,plain,(~c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),X1,X1)),inference(cn,[status(thm)],[57945,theory(equality)])).
% cnf(303506,plain,(c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))),inference(spm,[status(thm)],[11952,2600,theory(equality)])).
% cnf(309655,plain,(c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))|$false),inference(rw,[status(thm)],[24542,33570,theory(equality)])).
% cnf(309656,plain,(c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))),inference(cn,[status(thm)],[309655,theory(equality)])).
% cnf(332596,plain,(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),inference(spm,[status(thm)],[3665,50429,theory(equality)])).
% cnf(332625,plain,(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),hAPP(v_P,X1))),inference(spm,[status(thm)],[657,332596,theory(equality)])).
% cnf(334680,plain,(X1=X2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),hAPP(v_P,X3))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,X3))|~c_member(tc_Arrow__Order__Mirabelle_Oalt,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))|~c_member(tc_Arrow__Order__Mirabelle_Oalt,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),inference(spm,[status(thm)],[603,332625,theory(equality)])).
% cnf(334811,plain,(X1=X2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),hAPP(v_P,X3))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,X3))|$false|~c_member(tc_Arrow__Order__Mirabelle_Oalt,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),inference(rw,[status(thm)],[334680,2617,theory(equality)])).
% cnf(334812,plain,(X1=X2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),hAPP(v_P,X3))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,X3))|$false|$false),inference(rw,[status(thm)],[334811,2617,theory(equality)])).
% cnf(334813,plain,(X1=X2|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),hAPP(v_P,X3))|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,X3))),inference(cn,[status(thm)],[334812,theory(equality)])).
% cnf(709788,plain,(c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|$false),inference(rw,[status(thm)],[303506,309656,theory(equality)])).
% cnf(709789,plain,(c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))),inference(cn,[status(thm)],[709788,theory(equality)])).
% cnf(806735,plain,(v_b=v_a|$false|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))),inference(rw,[status(thm)],[23957,709789,theory(equality)])).
% cnf(806736,plain,(v_b=v_a|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P))),inference(cn,[status(thm)],[806735,theory(equality)])).
% cnf(806818,plain,(v_b=v_a|~c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i))),inference(spm,[status(thm)],[806736,2579,theory(equality)])).
% cnf(1030837,plain,(v_b=v_a|c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i))),inference(spm,[status(thm)],[806818,334813,theory(equality)])).
% cnf(1031095,plain,(v_b=v_a),inference(sr,[status(thm)],[1030837,2434,theory(equality)])).
% cnf(1031355,plain,(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_a)),inference(rw,[status(thm)],[3202,1031095,theory(equality)])).
% cnf(1031356,plain,($false),inference(sr,[status(thm)],[1031355,57946,theory(equality)])).
% cnf(1031357,plain,($false),1031356,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 11472
% # ...of these trivial : 1082
% # ...subsumed : 5532
% # ...remaining for further processing: 4858
% # Other redundant clauses eliminated : 4342
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 313
% # Backward-rewritten : 805
% # Generated clauses : 935765
% # ...of the previous two non-trivial : 895501
% # Contextual simplify-reflections : 630
% # Paramodulations : 931352
% # Factorizations : 20
% # Equation resolutions : 4391
% # Current number of processed clauses: 3062
% # Positive orientable unit clauses: 1670
% # Positive unorientable unit clauses: 14
% # Negative unit clauses : 174
% # Non-unit-clauses : 1204
% # Current number of unprocessed clauses: 335637
% # ...number of literals in the above : 953724
% # Clause-clause subsumption calls (NU) : 157388
% # Rec. Clause-clause subsumption calls : 121433
% # Unit Clause-clause subsumption calls : 16493
% # Rewrite failures with RHS unbound : 227
% # Indexed BW rewrite attempts : 491310
% # Indexed BW rewrite successes : 899
% # Backwards rewriting index: 1106 leaves, 5.73+/-23.718 terms/leaf
% # Paramod-from index: 444 leaves, 5.00+/-24.856 terms/leaf
% # Paramod-into index: 1000 leaves, 5.81+/-23.414 terms/leaf
% # -------------------------------------------------
% # User time : 33.572 s
% # System time : 0.906 s
% # Total time : 34.478 s
% # Maximum resident set size: 0 pages
% PrfWatch: 48.12 CPU 49.20 WC
% FINAL PrfWatch: 48.12 CPU 49.20 WC
% SZS output end Solution for /tmp/SystemOnTPTP9730/SCT122+1.tptp
%
%------------------------------------------------------------------------------