0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s 0.13/0.34 % Computer : n025.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 06:14:26 EDT 2022 0.13/0.34 % CPUTime : 0.20/0.45 openjdk version "1.8.0_171" 0.20/0.45 OpenJDK Runtime Environment (build 1.8.0_171-b10) 0.20/0.45 OpenJDK 64-Bit Server VM (build 25.171-b10, mixed mode) 0.20/0.45 file=/export/starexec/sandbox2/benchmark/theBenchmark.p 0.54/0.69 start to proof: theBenchmark 9.87/9.99 % Version : CSE_E---1.4 9.87/9.99 % Problem : theBenchmark.p 9.87/9.99 % Proof found 9.87/9.99 % SZS status Theorem for theBenchmark.p 9.87/9.99 % SZS output start Proof 9.87/9.99 fof(fact_insert__code, axiom, ![X3, X6, X2, X4]:(hBOOL(hAPP(c_Set_Oinsert(X4,X2,X6),X3))<=>(hBOOL(hAPP(X6,X3))|X3=X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__code)). 9.87/9.99 fof(fact_insert__absorb, axiom, ![X6, X9, X4]:(c_Set_Oinsert(X4,X9,X6)=X6<=c_member(X4,X9,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__absorb)). 9.87/9.99 fof(fact_irrefl__def, axiom, ![X5, X4]:(c_Relation_Oirrefl(X4,X5)<=>![X13]:~(c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X13),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__def)). 9.87/9.99 fof(fact_mem__def, axiom, ![X6, X3, X4]:(c_member(X4,X3,X6)<=>hBOOL(hAPP(X6,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__def)). 9.87/9.99 fof(conj_3, hypothesis, (![X13]:((c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X13))&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,X13)))&c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X13)))=>((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,v_F(v_P)))&c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_3)). 9.87/9.99 fof(conj_1, hypothesis, ![X13]:((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X13))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X13)))&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,X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_1)). 9.87/9.99 fof(fact_r__r__into__trancl, axiom, ![X35, X16, X8, X9, X4]:((c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X35),c_Transitive__Closure_Otrancl(X4,X16))<=c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X35),X16))<=c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__r__into__trancl)). 9.87/9.99 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/sandbox2/benchmark/theBenchmark.p', conj_2)). 9.87/9.99 fof(fact_trancl__id, axiom, ![X5, X4]:(c_Relation_Otrans(X4,X5)=>X5=c_Transitive__Closure_Otrancl(X4,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__id)). 9.87/9.99 fof(conj_0, hypothesis, ![X72]:(![X13]:((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X72,X13))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X72,X13)))&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(X72,X13)))=>![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),v_F(X72))<=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(X72,v_i)))<=X26!=X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_0)). 9.87/9.99 fof(fact_total__on__def, axiom, ![X5, X6, X4]:(c_Relation_Ototal__on(X4,X6,X5)<=>![X13]:(c_member(X4,X13,X6)=>![X68]:(c_member(X4,X68,X6)=>((c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X68),X5)|c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X68,X13),X5))<=X13!=X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__def)). 9.87/9.99 fof(fact_top1I, axiom, ![X3, X4]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top1I)). 9.87/9.99 fof(fact_acyclic__def, axiom, ![X5, X4]:(![X13]:~(c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X13),c_Transitive__Closure_Otrancl(X4,X5)))<=>c_Wellfounded_Oacyclic(X4,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__def)). 9.87/9.99 fof(fact_in__rel__def, axiom, ![X2, X3, X16, X7, X4]:(c_FunDef_Oin__rel(X4,X7,X16,X3,X2)<=>c_member(tc_prod(X4,X7),c_Product__Type_OPair(X4,X7,X3,X2),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__rel__def)). 9.87/9.99 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/sandbox2/benchmark/theBenchmark.p', conj_4)). 9.87/9.99 fof(c_0_15, plain, ![X2846, X2847, X2848, X2849]:((~hBOOL(hAPP(c_Set_Oinsert(X2849,X2848,X2847),X2846))|(hBOOL(hAPP(X2847,X2846))|X2846=X2848))&((~hBOOL(hAPP(X2847,X2846))|hBOOL(hAPP(c_Set_Oinsert(X2849,X2848,X2847),X2846)))&(X2846!=X2848|hBOOL(hAPP(c_Set_Oinsert(X2849,X2848,X2847),X2846))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])])). 9.87/9.99 fof(c_0_16, plain, ![X6, X9, X4]:(c_member(X4,X9,X6)=>c_Set_Oinsert(X4,X9,X6)=X6), inference(fof_simplification,[status(thm)],[fact_insert__absorb])). 9.87/9.99 cnf(c_0_17, plain, (hBOOL(hAPP(c_Set_Oinsert(X3,X2,X4),X1))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_15])). 9.87/9.99 fof(c_0_18, plain, ![X1984, X1985, X1986]:(~c_member(X1986,X1985,X1984)|c_Set_Oinsert(X1986,X1985,X1984)=X1984), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])). 9.87/9.99 fof(c_0_19, plain, ![X5, X4]:(c_Relation_Oirrefl(X4,X5)<=>![X13]:~c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X13),X5)), inference(fof_simplification,[status(thm)],[fact_irrefl__def])). 9.87/9.99 fof(c_0_20, plain, ![X3039, X3040, X3041]:((~c_member(X3041,X3040,X3039)|hBOOL(hAPP(X3039,X3040)))&(~hBOOL(hAPP(X3039,X3040))|c_member(X3041,X3040,X3039))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])). 9.87/9.99 cnf(c_0_21, plain, (hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2))), inference(er,[status(thm)],[c_0_17])). 9.87/9.99 cnf(c_0_22, plain, (c_Set_Oinsert(X1,X2,X3)=X3|~c_member(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_18])). 9.87/9.99 fof(c_0_23, 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)),v_F(v_P))|(~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_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,esk53_0))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_0))))&(c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|(~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_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,esk53_0))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_0)))))&(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|(~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_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,esk53_0))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_0))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])])). 9.87/9.99 fof(c_0_24, hypothesis, ![X3092]:((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3092))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3092)))&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,X3092))), inference(variable_rename,[status(thm)],[conj_1])). 9.87/9.99 fof(c_0_25, plain, ![X3392, X3393, X3394, X3395, X3396]:((~c_Relation_Oirrefl(X3393,X3392)|~c_member(tc_prod(X3393,X3393),c_Product__Type_OPair(X3393,X3393,X3394,X3394),X3392))&(c_member(tc_prod(X3396,X3396),c_Product__Type_OPair(X3396,X3396,esk60_2(X3395,X3396),esk60_2(X3395,X3396)),X3395)|c_Relation_Oirrefl(X3396,X3395))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])). 9.87/9.99 cnf(c_0_26, plain, (c_member(X3,X2,X1)|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_20])). 9.87/9.99 fof(c_0_27, plain, ![X35, X16, X8, X9, X4]:(c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X8),X16)=>(c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X8,X35),X16)=>c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X9,X35),c_Transitive__Closure_Otrancl(X4,X16)))), inference(fof_simplification,[status(thm)],[fact_r__r__into__trancl])). 9.87/9.99 cnf(c_0_28, plain, (hBOOL(hAPP(X1,X2))|~c_member(X3,X2,X1)), inference(spm,[status(thm)],[c_0_21, c_0_22])). 9.87/9.99 cnf(c_0_29, 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])). 9.87/9.99 fof(c_0_30, plain, ![X3684, X3685]:(~c_Relation_Otrans(X3685,X3684)|X3684=c_Transitive__Closure_Otrancl(X3685,X3684)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])])). 9.87/9.99 cnf(c_0_31, hypothesis, (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_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,esk53_0))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_0))), inference(split_conjunct,[status(thm)],[c_0_23])). 9.87/9.99 cnf(c_0_32, hypothesis, (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1))), inference(split_conjunct,[status(thm)],[c_0_24])). 9.87/9.99 cnf(c_0_33, hypothesis, (c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1))), inference(split_conjunct,[status(thm)],[c_0_24])). 9.87/9.99 cnf(c_0_34, 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_24])). 9.87/9.99 cnf(c_0_35, 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)],[c_0_25])). 9.87/9.99 cnf(c_0_36, plain, (c_member(X1,X2,c_Set_Oinsert(X3,X2,X4))), inference(spm,[status(thm)],[c_0_26, c_0_21])). 9.87/9.99 fof(c_0_37, plain, ![X3159, X3160, X3161, X3162, X3163]:(~c_member(tc_prod(X3163,X3163),c_Product__Type_OPair(X3163,X3163,X3162,X3161),X3160)|(~c_member(tc_prod(X3163,X3163),c_Product__Type_OPair(X3163,X3163,X3161,X3159),X3160)|c_member(tc_prod(X3163,X3163),c_Product__Type_OPair(X3163,X3163,X3162,X3159),c_Transitive__Closure_Otrancl(X3163,X3160)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])). 9.87/9.99 cnf(c_0_38, 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_28, c_0_29])). 9.87/9.99 cnf(c_0_39, plain, (X2=c_Transitive__Closure_Otrancl(X1,X2)|~c_Relation_Otrans(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_30])). 9.87/9.99 cnf(c_0_40, 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_31, c_0_32]), c_0_33]), c_0_34])])). 9.87/9.99 fof(c_0_41, hypothesis, ![X72]:(![X13]:((c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X72,X13))&c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X72,X13)))&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(X72,X13)))=>![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(X72,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(X72))))), inference(fof_simplification,[status(thm)],[conj_0])). 9.87/9.99 cnf(c_0_42, plain, (~c_Relation_Oirrefl(X1,c_Set_Oinsert(X2,c_Product__Type_OPair(X1,X1,X3,X3),X4))), inference(spm,[status(thm)],[c_0_35, c_0_36])). 9.87/9.99 cnf(c_0_43, plain, (c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X5),c_Transitive__Closure_Otrancl(X1,X4))|~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,X5),X4)), inference(split_conjunct,[status(thm)],[c_0_37])). 9.87/9.99 cnf(c_0_44, 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_26, c_0_38])). 9.87/9.99 cnf(c_0_45, hypothesis, (c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))=v_F(v_P)), inference(spm,[status(thm)],[c_0_39, c_0_40])). 9.87/9.99 cnf(c_0_46, hypothesis, (c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_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,esk53_0))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk53_0))), inference(split_conjunct,[status(thm)],[c_0_23])). 9.87/9.99 fof(c_0_47, hypothesis, ![X3649, X3653, X3654]:(~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3649,esk74_1(X3649)))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3649,esk75_1(X3649)))|~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(X3649,esk76_1(X3649)))|(X3653=X3654|(~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,X3653,X3654),hAPP(X3649,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,X3653,X3654),v_F(X3649))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])])). 9.87/9.99 fof(c_0_48, plain, ![X5, X6, X4]:(c_Relation_Ototal__on(X4,X6,X5)<=>![X13]:(c_member(X4,X13,X6)=>![X68]:(c_member(X4,X68,X6)=>(X13!=X68=>(c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X68),X5)|c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X68,X13),X5)))))), inference(fof_simplification,[status(thm)],[fact_total__on__def])). 9.87/9.99 fof(c_0_49, plain, ![X3775, X3776]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3776,tc_HOL_Obool)),X3775)), inference(variable_rename,[status(thm)],[fact_top1I])). 9.87/9.99 fof(c_0_50, plain, ![X5, X4]:(![X13]:~c_member(tc_prod(X4,X4),c_Product__Type_OPair(X4,X4,X13,X13),c_Transitive__Closure_Otrancl(X4,X5))<=>c_Wellfounded_Oacyclic(X4,X5)), inference(fof_simplification,[status(thm)],[fact_acyclic__def])). 9.87/9.99 cnf(c_0_51, plain, (~c_Relation_Oirrefl(X1,X2)|~c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2)), inference(spm,[status(thm)],[c_0_42, c_0_22])). 9.87/9.99 cnf(c_0_52, 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_45])). 9.87/9.99 cnf(c_0_53, 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_46, c_0_32]), c_0_33]), c_0_34])])). 9.87/10.00 cnf(c_0_54, hypothesis, (X2=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,X2,X3),v_F(X1))|~c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk74_1(X1)))|~c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk75_1(X1)))|~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(X1,esk76_1(X1)))|~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,X3),hAPP(X1,v_i))), inference(split_conjunct,[status(thm)],[c_0_47])). 9.87/10.00 fof(c_0_55, plain, ![X3701, X3702, X3703, X3704, X3705, X3706, X3707, X3708]:((~c_Relation_Ototal__on(X3703,X3702,X3701)|(~c_member(X3703,X3704,X3702)|(~c_member(X3703,X3705,X3702)|(X3704=X3705|(c_member(tc_prod(X3703,X3703),c_Product__Type_OPair(X3703,X3703,X3704,X3705),X3701)|c_member(tc_prod(X3703,X3703),c_Product__Type_OPair(X3703,X3703,X3705,X3704),X3701))))))&((c_member(X3708,esk79_3(X3706,X3707,X3708),X3707)|c_Relation_Ototal__on(X3708,X3707,X3706))&((c_member(X3708,esk80_3(X3706,X3707,X3708),X3707)|c_Relation_Ototal__on(X3708,X3707,X3706))&((esk79_3(X3706,X3707,X3708)!=esk80_3(X3706,X3707,X3708)|c_Relation_Ototal__on(X3708,X3707,X3706))&((~c_member(tc_prod(X3708,X3708),c_Product__Type_OPair(X3708,X3708,esk79_3(X3706,X3707,X3708),esk80_3(X3706,X3707,X3708)),X3706)|c_Relation_Ototal__on(X3708,X3707,X3706))&(~c_member(tc_prod(X3708,X3708),c_Product__Type_OPair(X3708,X3708,esk80_3(X3706,X3707,X3708),esk79_3(X3706,X3707,X3708)),X3706)|c_Relation_Ototal__on(X3708,X3707,X3706))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])])])])). 9.87/10.00 cnf(c_0_56, plain, (hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_49])). 9.87/10.00 fof(c_0_57, plain, ![X2034, X2035, X2037, X2038, X2039]:((c_member(tc_prod(X2035,X2035),c_Product__Type_OPair(X2035,X2035,esk8_2(X2034,X2035),esk8_2(X2034,X2035)),c_Transitive__Closure_Otrancl(X2035,X2034))|c_Wellfounded_Oacyclic(X2035,X2034))&(~c_Wellfounded_Oacyclic(X2038,X2037)|~c_member(tc_prod(X2038,X2038),c_Product__Type_OPair(X2038,X2038,X2039,X2039),c_Transitive__Closure_Otrancl(X2038,X2037)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])])). 9.87/10.00 fof(c_0_58, plain, ![X3436, X3437, X3438, X3439, X3440]:((~c_FunDef_Oin__rel(X3440,X3439,X3438,X3437,X3436)|c_member(tc_prod(X3440,X3439),c_Product__Type_OPair(X3440,X3439,X3437,X3436),X3438))&(~c_member(tc_prod(X3440,X3439),c_Product__Type_OPair(X3440,X3439,X3437,X3436),X3438)|c_FunDef_Oin__rel(X3440,X3439,X3438,X3437,X3436))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])])). 9.87/10.00 cnf(c_0_59, 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_51, c_0_52]), c_0_53])])). 9.87/10.00 cnf(c_0_60, 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_54, c_0_34]), c_0_33]), c_0_32])])). 9.87/10.00 cnf(c_0_61, plain, (X4=X5|c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X3)|c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X3)|~c_Relation_Ototal__on(X1,X2,X3)|~c_member(X1,X4,X2)|~c_member(X1,X5,X2)), inference(split_conjunct,[status(thm)],[c_0_55])). 9.87/10.00 cnf(c_0_62, plain, (c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), inference(spm,[status(thm)],[c_0_26, c_0_56])). 9.87/10.00 fof(c_0_63, 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)],[inference(assume_negation,[status(cth)],[conj_4])])). 9.87/10.00 cnf(c_0_64, plain, (c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,esk8_2(X2,X1),esk8_2(X2,X1)),c_Transitive__Closure_Otrancl(X1,X2))|c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_57])). 9.87/10.00 cnf(c_0_65, plain, (c_FunDef_Oin__rel(X1,X2,X5,X3,X4)|~c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X3,X4),X5)), inference(split_conjunct,[status(thm)],[c_0_58])). 9.87/10.00 cnf(c_0_66, 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_59, c_0_60])). 9.87/10.00 cnf(c_0_67, 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),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,X2,X1),hAPP(v_P,X3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_34]), c_0_62]), c_0_62])])). 9.87/10.00 cnf(c_0_68, 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_63])). 9.87/10.00 cnf(c_0_69, 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)],[c_0_57])). 9.87/10.00 cnf(c_0_70, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Relation_Oirrefl(X1,c_Transitive__Closure_Otrancl(X1,X2))), inference(spm,[status(thm)],[c_0_35, c_0_64])). 9.87/10.00 cnf(c_0_71, 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_65, c_0_44])). 9.87/10.00 cnf(c_0_72, hypothesis, (v_b=v_a), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_68])). 9.87/10.00 cnf(c_0_73, hypothesis, (~c_Wellfounded_Oacyclic(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,X1,X1),v_F(v_P))), inference(spm,[status(thm)],[c_0_69, c_0_45])). 9.87/10.00 cnf(c_0_74, 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_70, c_0_45]), c_0_53])])). 9.87/10.00 cnf(c_0_75, plain, (c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X4,X5),X3)|~c_FunDef_Oin__rel(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_58])). 9.87/10.00 cnf(c_0_76, 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_71, c_0_72])). 9.87/10.00 cnf(c_0_77, 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,X1),v_F(v_P))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_74])])). 9.87/10.00 cnf(c_0_78, hypothesis, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76]), c_0_77]), ['proof']). 9.87/10.00 % SZS output end Proof 9.87/10.00 % Total time : 9.287000 s 9.97/10.01 EOF