0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -jar mcs_epr.jar %d %s 0.03/0.23 % Computer : n018.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:44:09 CDT 2018 0.03/0.23 % CPUTime : 0.06/0.30 openjdk version "1.8.0_144" 0.06/0.30 OpenJDK Runtime Environment (build 1.8.0_144-b01) 0.06/0.30 OpenJDK 64-Bit Server VM (build 25.144-b01, mixed mode) 0.14/0.40 start to proof:theBenchmark.p 132.01/132.01 % Version : CSE_E---1.0 132.01/132.01 % Problem : theBenchmark.p 132.01/132.01 % Proof found! 132.01/132.01 % SZS status Theorem for theBenchmark.p 132.01/132.01 % SZS output start Proof 132.01/132.01 fof(fact_mem__def, axiom, (![X4]:![X20]:![X5]:(hBOOL(hAPP(X4,X20))<=>c_member(X5,X20,X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_mem__def)). 132.01/132.01 fof(fact_insertI1, axiom, (![X3]:![X9]:![X5]:c_member(X5,X9,c_Set_Oinsert(X5,X9,X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_insertI1)). 132.01/132.01 fof(fact_reflcl__trancl, axiom, (![X17]:![X5]:c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X5,X17),c_Relation_OId(X5))=c_Transitive__Closure_Ortrancl(X5,X17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_reflcl__trancl)). 132.01/132.01 fof(fact_rtrancl__empty, 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('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_rtrancl__empty)). 132.01/132.01 fof(conj_3, hypothesis, ((![X10]:((c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X10))&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,X10)))&c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X10)))=>((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('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_3)). 132.01/132.01 fof(conj_1, hypothesis, (![X10]:((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,X10))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X10)))&c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X10)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_1)). 132.01/132.01 fof(fact_Un__upper1, axiom, (![X3]:![X4]:![X5]:c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool),X4,X3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_Un__upper1)). 132.01/132.01 fof(fact_trancl__id, axiom, (![X17]:![X5]:(X17=c_Transitive__Closure_Otrancl(X5,X17)<=c_Relation_Otrans(X5,X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_trancl__id)). 132.01/132.01 fof(fact_irrefl__def, axiom, (![X17]:![X5]:(c_Relation_Oirrefl(X5,X17)<=>![X10]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X10,X10),X17)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_irrefl__def)). 132.01/132.01 fof(fact_insert__absorb, axiom, (![X4]:![X9]:![X5]:(c_member(X5,X9,X4)=>c_Set_Oinsert(X5,X9,X4)=X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_insert__absorb)). 132.01/132.01 fof(fact_antisym__subset, axiom, (![X24]:![X17]:![X5]:((c_Relation_Oantisym(X5,X17)<=c_Relation_Oantisym(X5,X24))<=c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X17,X24))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_antisym__subset)). 132.01/132.01 fof(fact_acyclicI, axiom, (![X17]:![X5]:(![X10]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X10,X10),c_Transitive__Closure_Otrancl(X5,X17)))=>c_Wellfounded_Oacyclic(X5,X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_acyclicI)). 132.01/132.01 fof(fact_top__apply, axiom, (![X20]:![X12]:![X5]:(class_Orderings_Otop(X5)=>hAPP(c_Orderings_Otop__class_Otop(tc_fun(X12,X5)),X20)=c_Orderings_Otop__class_Otop(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_top__apply)). 132.01/132.01 fof(fact_acyclic__impl__antisym__rtrancl, axiom, (![X17]:![X5]:(c_Relation_Oantisym(X5,c_Transitive__Closure_Ortrancl(X5,X17))<=c_Wellfounded_Oacyclic(X5,X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_acyclic__impl__antisym__rtrancl)). 132.01/132.01 fof(fact_ext, axiom, (![X34]:![X21]:(![X10]:hAPP(X21,X10)=hAPP(X34,X10)=>X21=X34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_ext)). 132.01/132.01 fof(arity_HOL__Obool__Orderings_Otop, axiom, (class_Orderings_Otop(tc_HOL_Obool)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Otop)). 132.01/132.01 fof(fact_r__into__trancl_H, axiom, (![X17]:![X41]:![X5]:(c_member(tc_prod(X5,X5),X41,c_Transitive__Closure_Otrancl(X5,X17))<=c_member(tc_prod(X5,X5),X41,X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_r__into__trancl_H)). 132.01/132.01 fof(conj_2, hypothesis, (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('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_2)). 132.01/132.01 fof(fact_antisymD, axiom, (![X8]:![X9]:![X17]:![X5]:((c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X9,X8),X17)=>(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X8,X9),X17)=>X8=X9))<=c_Relation_Oantisym(X5,X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_antisymD)). 132.01/132.01 fof(conj_0, hypothesis, (![X46]:(![X14]:![X15]:((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,X14,X15),v_F(X46))<=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,X14,X15),hAPP(X46,v_i)))<=X14!=X15)<=![X10]:((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(X46,X10))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X46,X10)))&c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X46,X10))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_0)). 132.01/132.01 fof(fact_top1I, axiom, (![X20]:![X5]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X20))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_top1I)). 132.01/132.01 fof(fact_acyclic__def, axiom, (![X17]:![X5]:(c_Wellfounded_Oacyclic(X5,X17)<=>![X10]:~(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X10,X10),c_Transitive__Closure_Otrancl(X5,X17))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_acyclic__def)). 132.01/132.01 fof(fact_total__on__def, axiom, (![X17]:![X4]:![X5]:(c_Relation_Ototal__on(X5,X4,X17)<=>![X10]:(![X22]:(c_member(X5,X22,X4)=>((c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X22,X10),X17)|c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X10,X22),X17))<=X22!=X10))<=c_member(X5,X10,X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_total__on__def)). 132.01/132.01 fof(conj_4, 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('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_4)). 132.01/132.01 fof(fact_trans__def, axiom, (![X17]:![X5]:(c_Relation_Otrans(X5,X17)<=>![X10]:![X11]:(![X23]:(c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X11,X23),X17)=>c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X10,X23),X17))<=c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X10,X11),X17)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_trans__def)). 132.01/132.01 fof(fact_in__rel__def, axiom, (![X27]:![X20]:![X29]:![X12]:![X5]:(c_FunDef_Oin__rel(X5,X12,X29,X20,X27)<=>c_member(tc_prod(X5,X12),c_Product__Type_OPair(X5,X12,X20,X27),X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_in__rel__def)). 132.01/132.01 fof(c_0_26, plain, (![X21]:![X22]:![X23]:![X21]:![X22]:![X23]:((~hBOOL(hAPP(X21,X22))|c_member(X23,X22,X21))&(~c_member(X23,X22,X21)|hBOOL(hAPP(X21,X22))))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])])])). 132.01/132.01 fof(c_0_27, plain, (![X10]:![X11]:![X12]:c_member(X12,X11,c_Set_Oinsert(X12,X11,X10))), inference(variable_rename,[status(thm)],[fact_insertI1])). 132.01/132.01 fof(c_0_28, plain, (![X18]:![X19]:c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X19,X19),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X19,X18),c_Relation_OId(X19))=c_Transitive__Closure_Ortrancl(X19,X18)), inference(variable_rename,[status(thm)],[fact_reflcl__trancl])). 132.01/132.01 fof(c_0_29, 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)],[fact_rtrancl__empty])). 132.01/132.01 fof(c_0_30, hypothesis, ((((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|((~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk79_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,esk80_0)))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk81_0))))&(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|((~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk79_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,esk80_0)))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk81_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_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk79_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,esk80_0)))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk81_0)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])])])])). 132.01/132.01 fof(c_0_31, hypothesis, (![X11]:![X11]:![X11]:((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,X11))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X11)))&c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X11)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[conj_1])])])). 132.01/132.01 cnf(c_0_32,plain,(hBOOL(hAPP(X1,X2))|~c_member(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_26])). 132.01/132.01 cnf(c_0_33,plain,(c_member(X1,X2,c_Set_Oinsert(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_27])). 132.01/132.01 fof(c_0_34, plain, (![X6]:![X7]:![X8]:c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X7,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool),X7,X6))), inference(variable_rename,[status(thm)],[fact_Un__upper1])). 132.01/132.01 cnf(c_0_35,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)],[c_0_28])). 132.01/132.01 cnf(c_0_36,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)],[c_0_29])). 132.01/132.01 fof(c_0_37, plain, (![X18]:![X19]:(~c_Relation_Otrans(X19,X18)|X18=c_Transitive__Closure_Otrancl(X19,X18))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__id])])])). 132.01/132.01 cnf(c_0_38,hypothesis,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk81_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,esk80_0))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk79_0))), inference(split_conjunct,[status(thm)],[c_0_30])). 132.01/132.01 cnf(c_0_39,hypothesis,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1))), inference(split_conjunct,[status(thm)],[c_0_31])). 132.01/132.01 cnf(c_0_40,hypothesis,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1))), inference(split_conjunct,[status(thm)],[c_0_31])). 132.01/132.01 cnf(c_0_41,hypothesis,(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)],[c_0_31])). 132.01/132.01 fof(c_0_42, plain, (![X18]:![X19]:![X20]:![X18]:![X19]:((~c_Relation_Oirrefl(X19,X18)|~c_member(tc_prod(X19,X19),c_Product__Type_OPair(X19,X19,X20,X20),X18))&(c_member(tc_prod(X19,X19),c_Product__Type_OPair(X19,X19,esk36_2(X18,X19),esk36_2(X18,X19)),X18)|c_Relation_Oirrefl(X19,X18)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_irrefl__def])])])])])])])). 132.01/132.01 cnf(c_0_43,plain,(c_member(X1,X2,X3)|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_26])). 132.01/132.01 cnf(c_0_44,plain,(hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2))), inference(spm,[status(thm)],[c_0_32, c_0_33])). 132.01/132.01 cnf(c_0_45,plain,(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool),X2,X3))), inference(split_conjunct,[status(thm)],[c_0_34])). 132.01/132.01 cnf(c_0_46,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)],[c_0_35, c_0_36])). 132.01/132.01 cnf(c_0_47,plain,(X1=c_Transitive__Closure_Otrancl(X2,X1)|~c_Relation_Otrans(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_37])). 132.01/132.01 cnf(c_0_48,hypothesis,(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39]), c_0_40]), c_0_41])])). 132.01/132.01 cnf(c_0_49,plain,(~c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),X3)|~c_Relation_Oirrefl(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_42])). 132.01/132.01 cnf(c_0_50,plain,(c_member(X1,X2,c_Set_Oinsert(X3,X2,X4))), inference(spm,[status(thm)],[c_0_43, c_0_44])). 132.01/132.01 fof(c_0_51, plain, (![X10]:![X11]:![X12]:(~c_member(X12,X11,X10)|c_Set_Oinsert(X12,X11,X10)=X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])])). 132.01/132.01 fof(c_0_52, plain, (![X25]:![X26]:![X27]:(~c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27,X27),tc_HOL_Obool),X26,X25)|(~c_Relation_Oantisym(X27,X25)|c_Relation_Oantisym(X27,X26)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_antisym__subset])])])). 132.01/132.01 cnf(c_0_53,plain,(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Otrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2))), inference(spm,[status(thm)],[c_0_45, c_0_46])). 132.01/132.01 cnf(c_0_54,hypothesis,(c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))=v_F(v_P)), inference(spm,[status(thm)],[c_0_47, c_0_48])). 132.01/132.01 cnf(c_0_55,plain,(~c_Relation_Oirrefl(X1,c_Set_Oinsert(X2,c_Product__Type_OPair(X1,X1,X3,X3),X4))), inference(spm,[status(thm)],[c_0_49, c_0_50])). 132.01/132.01 cnf(c_0_56,plain,(c_Set_Oinsert(X1,X2,X3)=X3|~c_member(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_51])). 132.01/132.01 fof(c_0_57, plain, (![X18]:![X19]:(c_member(tc_prod(X19,X19),c_Product__Type_OPair(X19,X19,esk46_2(X18,X19),esk46_2(X18,X19)),c_Transitive__Closure_Otrancl(X19,X18))|c_Wellfounded_Oacyclic(X19,X18))), inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclicI])])])])])])). 132.01/132.01 fof(c_0_58, plain, (![X21]:![X22]:![X23]:(~class_Orderings_Otop(X23)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(X22,X23)),X21)=c_Orderings_Otop__class_Otop(X23))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])])). 132.01/132.01 cnf(c_0_59,plain,(c_Relation_Oantisym(X1,X2)|~c_Relation_Oantisym(X1,X3)|~c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_52])). 132.01/132.01 cnf(c_0_60,hypothesis,(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),v_F(v_P),c_Transitive__Closure_Ortrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))), inference(spm,[status(thm)],[c_0_53, c_0_54])). 132.01/132.01 fof(c_0_61, plain, (![X18]:![X19]:(~c_Wellfounded_Oacyclic(X19,X18)|c_Relation_Oantisym(X19,c_Transitive__Closure_Ortrancl(X19,X18)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__impl__antisym__rtrancl])])])). 132.01/132.01 cnf(c_0_62,plain,(~c_Relation_Oirrefl(X1,X2)|~c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2)), inference(spm,[status(thm)],[c_0_55, c_0_56])). 132.01/132.01 cnf(c_0_63,plain,(c_Wellfounded_Oacyclic(X1,X2)|c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,esk46_2(X2,X1),esk46_2(X2,X1)),c_Transitive__Closure_Otrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_57])). 132.01/132.01 cnf(c_0_64,hypothesis,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk81_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,esk80_0))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk79_0))), inference(split_conjunct,[status(thm)],[c_0_30])). 132.01/132.01 fof(c_0_65, plain, (![X35]:![X36]:(hAPP(X36,esk30_2(X35,X36))!=hAPP(X35,esk30_2(X35,X36))|X36=X35)), inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])])])). 132.01/132.01 cnf(c_0_66,plain,(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X3)=c_Orderings_Otop__class_Otop(X2)|~class_Orderings_Otop(X2)), inference(split_conjunct,[status(thm)],[c_0_58])). 132.01/132.01 cnf(c_0_67,plain,(class_Orderings_Otop(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop])). 132.01/132.01 fof(c_0_68, plain, (![X42]:![X43]:![X44]:(~c_member(tc_prod(X44,X44),X43,X42)|c_member(tc_prod(X44,X44),X43,c_Transitive__Closure_Otrancl(X44,X42)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_r__into__trancl_H])])])). 132.01/132.01 cnf(c_0_69,hypothesis,(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)],[conj_2])). 132.01/132.01 cnf(c_0_70,hypothesis,(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)],[c_0_59, c_0_60])). 132.01/132.01 cnf(c_0_71,plain,(c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_61])). 132.01/132.01 cnf(c_0_72,plain,(c_Wellfounded_Oacyclic(X1,X2)|~c_Relation_Oirrefl(X1,c_Transitive__Closure_Otrancl(X1,X2))), inference(spm,[status(thm)],[c_0_62, c_0_63])). 132.01/132.01 cnf(c_0_73,hypothesis,(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_39]), c_0_40]), c_0_41])])). 132.01/132.01 cnf(c_0_74,plain,(X1=X2|hAPP(X1,esk30_2(X2,X1))!=hAPP(X2,esk30_2(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_65])). 132.01/132.01 cnf(c_0_75,plain,(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)=c_Orderings_Otop__class_Otop(tc_HOL_Obool)), inference(spm,[status(thm)],[c_0_66, c_0_67])). 132.01/132.01 cnf(c_0_76,plain,(c_member(X1,X2,X3)|~c_member(X4,X2,X3)), inference(spm,[status(thm)],[c_0_50, c_0_56])). 132.01/132.01 cnf(c_0_77,plain,(c_member(tc_prod(X1,X1),X2,c_Transitive__Closure_Otrancl(X1,X3))|~c_member(tc_prod(X1,X1),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_68])). 132.01/132.01 fof(c_0_78, plain, (![X18]:![X19]:![X20]:![X21]:(~c_Relation_Oantisym(X21,X20)|(~c_member(tc_prod(X21,X21),c_Product__Type_OPair(X21,X21,X19,X18),X20)|(~c_member(tc_prod(X21,X21),c_Product__Type_OPair(X21,X21,X18,X19),X20)|X18=X19)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_antisymD])])])). 132.01/132.01 cnf(c_0_79,hypothesis,(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)],[c_0_32, c_0_69])). 132.01/132.01 cnf(c_0_80,hypothesis,(c_Relation_Oantisym(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)],[c_0_70, c_0_71])). 132.01/132.01 cnf(c_0_81,hypothesis,(c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_54]), c_0_73])])). 132.01/132.01 fof(c_0_82, hypothesis, (![X47]:![X49]:![X50]:(((~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(X47,esk25_1(X47)))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X47,esk26_1(X47))))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X47,esk27_1(X47))))|(X49=X50|(~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,X49,X50),hAPP(X47,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,X49,X50),v_F(X47)))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[conj_0])])])])])])])). 132.01/132.01 cnf(c_0_83,plain,(X1=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(X1,esk30_2(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1))!=c_Orderings_Otop__class_Otop(tc_HOL_Obool)), inference(spm,[status(thm)],[c_0_74, c_0_75])). 132.01/132.01 fof(c_0_84, plain, (![X21]:![X22]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X22,tc_HOL_Obool)),X21))), inference(variable_rename,[status(thm)],[fact_top1I])). 132.01/132.01 fof(c_0_85, plain, (![X18]:![X19]:![X20]:![X18]:![X19]:((~c_Wellfounded_Oacyclic(X19,X18)|~c_member(tc_prod(X19,X19),c_Product__Type_OPair(X19,X19,X20,X20),c_Transitive__Closure_Otrancl(X19,X18)))&(c_member(tc_prod(X19,X19),c_Product__Type_OPair(X19,X19,esk50_2(X18,X19),esk50_2(X18,X19)),c_Transitive__Closure_Otrancl(X19,X18))|c_Wellfounded_Oacyclic(X19,X18)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__def])])])])])])])). 132.01/132.01 cnf(c_0_86,plain,(c_member(X1,X2,c_Transitive__Closure_Otrancl(X3,X4))|~c_member(tc_prod(X3,X3),X2,X4)), inference(spm,[status(thm)],[c_0_76, c_0_77])). 132.01/132.01 cnf(c_0_87,plain,(X1=X2|~c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X1,X2),X4)|~c_member(tc_prod(X3,X3),c_Product__Type_OPair(X3,X3,X2,X1),X4)|~c_Relation_Oantisym(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_78])). 132.01/132.01 cnf(c_0_88,hypothesis,(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)],[c_0_43, c_0_79])). 132.01/132.01 cnf(c_0_89,hypothesis,(c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])). 132.01/132.01 cnf(c_0_90,hypothesis,(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(X3))|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),hAPP(X3,v_i))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3,esk27_1(X3)))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3,esk26_1(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(X3,esk25_1(X3)))), inference(split_conjunct,[status(thm)],[c_0_82])). 132.01/132.01 fof(c_0_91, plain, (![X23]:![X24]:![X25]:![X26]:![X27]:![X23]:![X24]:![X25]:((~c_Relation_Ototal__on(X25,X24,X23)|(~c_member(X25,X26,X24)|(~c_member(X25,X27,X24)|(X27=X26|(c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,X27,X26),X23)|c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,X26,X27),X23))))))&((c_member(X25,esk87_3(X23,X24,X25),X24)|c_Relation_Ototal__on(X25,X24,X23))&((c_member(X25,esk88_3(X23,X24,X25),X24)|c_Relation_Ototal__on(X25,X24,X23))&((esk88_3(X23,X24,X25)!=esk87_3(X23,X24,X25)|c_Relation_Ototal__on(X25,X24,X23))&((~c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,esk88_3(X23,X24,X25),esk87_3(X23,X24,X25)),X23)|c_Relation_Ototal__on(X25,X24,X23))&(~c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,esk87_3(X23,X24,X25),esk88_3(X23,X24,X25)),X23)|c_Relation_Ototal__on(X25,X24,X23)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_total__on__def])])])])])])])])). 132.01/132.01 cnf(c_0_92,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)],[c_0_83, c_0_75])). 132.01/132.01 cnf(c_0_93,plain,(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_84])). 132.01/132.01 fof(c_0_94, 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)],[conj_4])). 132.01/132.01 cnf(c_0_95,plain,(~c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X1,X3))|~c_Wellfounded_Oacyclic(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_85])). 132.01/132.01 cnf(c_0_96,plain,(c_member(X1,X2,c_Transitive__Closure_Otrancl(X3,c_Set_Oinsert(X4,X2,X5)))), inference(spm,[status(thm)],[c_0_86, c_0_50])). 132.01/132.01 fof(c_0_97, plain, (![X24]:![X25]:![X26]:![X27]:![X28]:![X24]:![X25]:((~c_Relation_Otrans(X25,X24)|(~c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,X26,X27),X24)|(~c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,X27,X28),X24)|c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,X26,X28),X24))))&((c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,esk54_2(X24,X25),esk55_2(X24,X25)),X24)|c_Relation_Otrans(X25,X24))&((c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,esk55_2(X24,X25),esk56_2(X24,X25)),X24)|c_Relation_Otrans(X25,X24))&(~c_member(tc_prod(X25,X25),c_Product__Type_OPair(X25,X25,esk54_2(X24,X25),esk56_2(X24,X25)),X24)|c_Relation_Otrans(X25,X24)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__def])])])])])])])])). 132.01/132.01 fof(c_0_98, plain, (![X30]:![X31]:![X32]:![X33]:![X34]:![X30]:![X31]:![X32]:![X33]:![X34]:((~c_FunDef_Oin__rel(X34,X33,X32,X31,X30)|c_member(tc_prod(X34,X33),c_Product__Type_OPair(X34,X33,X31,X30),X32))&(~c_member(tc_prod(X34,X33),c_Product__Type_OPair(X34,X33,X31,X30),X32)|c_FunDef_Oin__rel(X34,X33,X32,X31,X30)))), inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])])])])). 132.01/132.01 cnf(c_0_99,hypothesis,(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)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_89])])). 132.01/132.01 cnf(c_0_100,hypothesis,(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_41]), c_0_40]), c_0_39])])). 132.01/132.01 cnf(c_0_101,plain,(c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X4)|c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X2),X4)|X3=X2|~c_member(X1,X3,X5)|~c_member(X1,X2,X5)|~c_Relation_Ototal__on(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_91])). 132.01/132.01 cnf(c_0_102,hypothesis,(c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(v_P,X2))), inference(spm,[status(thm)],[c_0_41, c_0_92])). 132.01/132.01 cnf(c_0_103,plain,(c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), inference(spm,[status(thm)],[c_0_43, c_0_93])). 132.01/132.01 fof(c_0_104, 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)],[c_0_94])). 132.01/132.01 cnf(c_0_105,plain,(~c_Wellfounded_Oacyclic(X1,c_Set_Oinsert(X2,c_Product__Type_OPair(X1,X1,X3,X3),X4))), inference(spm,[status(thm)],[c_0_95, c_0_96])). 132.01/132.01 cnf(c_0_106,plain,(c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X4)|~c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X3),X4)|~c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X5),X4)|~c_Relation_Otrans(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_97])). 132.01/132.01 cnf(c_0_107,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)],[c_0_98])). 132.01/132.01 cnf(c_0_108,hypothesis,(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)],[c_0_99, c_0_100])). 132.01/132.01 cnf(c_0_109,hypothesis,(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102]), c_0_103]), c_0_103])])). 132.01/132.01 cnf(c_0_110,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)],[c_0_104])). 132.01/132.01 cnf(c_0_111,plain,(~c_Wellfounded_Oacyclic(X1,X2)|~c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2)), inference(spm,[status(thm)],[c_0_105, c_0_56])). 132.01/132.01 cnf(c_0_112,hypothesis,(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,v_b),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,v_a),v_F(v_P))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_88]), c_0_48])])). 132.01/132.01 cnf(c_0_113,hypothesis,(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)],[c_0_107, c_0_88])). 132.01/132.01 cnf(c_0_114,hypothesis,(v_b=v_a), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_110])). 132.01/132.01 cnf(c_0_115,hypothesis,(~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)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_112]), c_0_81])])). 132.01/132.01 cnf(c_0_116,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)],[c_0_98])). 132.01/132.01 cnf(c_0_117,hypothesis,(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)],[c_0_113, c_0_114])). 132.01/132.01 cnf(c_0_118,hypothesis,(~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_a),v_F(v_P))), inference(rw,[status(thm)],[c_0_115, c_0_114])). 132.01/132.01 cnf(c_0_119,hypothesis,($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117]), c_0_118]), ['proof']). 132.01/132.01 % SZS output end Proof 132.01/132.01 % User time : 128.144 s 132.01/132.01 % System time : 3.383 s 132.01/132.01 % Total time : 131.526 s 132.01/132.01 132.05/132.02 EOF