TSTP Solution File: SCT122+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:16:48 EDT 2023
% Result : Theorem 137.35s 18.06s
% Output : CNFRefutation 137.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 27 unt; 0 def)
% Number of atoms : 201 ( 23 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 205 ( 81 ~; 82 |; 23 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-5 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-4 aty)
% Number of variables : 177 ( 24 sgn; 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_insert__code,axiom,
! [X4,X7,X17,X5] :
( hBOOL(hAPP(c_Set_Oinsert(X5,X17,X7),X4))
<=> ( X17 = X4
| hBOOL(hAPP(X7,X4)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_insert__code) ).
fof(fact_insert__absorb,axiom,
! [X7,X13,X5] :
( c_member(X5,X13,X7)
=> c_Set_Oinsert(X5,X13,X7) = X7 ),
file('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_insert__absorb) ).
fof(fact_irrefl__def,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('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_irrefl__def) ).
fof(fact_mem__def,axiom,
! [X7,X4,X5] :
( c_member(X5,X4,X7)
<=> hBOOL(hAPP(X7,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_mem__def) ).
fof(conj_2,hypothesis,
( ! [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('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',conj_2) ).
fof(conj_0,hypothesis,
! [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('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',conj_0) ).
fof(conj_1,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/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',conj_1) ).
fof(fact_trancl__id,axiom,
! [X6,X5] :
( c_Relation_Otrans(X5,X6)
=> c_Transitive__Closure_Otrancl(X5,X6) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_trancl__id) ).
fof(fact_r__r__into__trancl,axiom,
! [X11,X19,X12,X13,X5] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X13,X12),X19)
=> ( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X12,X11),X19)
=> c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X13,X11),c_Transitive__Closure_Otrancl(X5,X19)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_r__r__into__trancl) ).
fof(conj_3,hypothesis,
( ! [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)) )
=> ! [X38,X39] :
( X38 != X39
=> ( 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,X38,X39),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,X38,X39),v_F(v_P)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',conj_3) ).
fof(fact_top1I,axiom,
! [X4,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X4)),
file('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_top1I) ).
fof(fact_acyclic__def,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('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_acyclic__def) ).
fof(fact_total__on__def,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('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_total__on__def) ).
fof(fact_in__rel__def,axiom,
! [X17,X4,X19,X18,X5] :
( c_FunDef_Oin__rel(X5,X18,X19,X4,X17)
<=> c_member(tc_prod(X5,X18),c_Product__Type_OPair(X5,X18,X4,X17),X19) ),
file('/export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',fact_in__rel__def) ).
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/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p',conj_4) ).
fof(c_0_15,plain,
! [X955,X956,X957,X958] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X958,X957,X956),X955))
| X957 = X955
| hBOOL(hAPP(X956,X955)) )
& ( X957 != X955
| hBOOL(hAPP(c_Set_Oinsert(X958,X957,X956),X955)) )
& ( ~ hBOOL(hAPP(X956,X955))
| hBOOL(hAPP(c_Set_Oinsert(X958,X957,X956),X955)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
cnf(c_0_16,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_17,plain,
! [X944,X945,X946] :
( ~ c_member(X946,X945,X944)
| c_Set_Oinsert(X946,X945,X944) = X944 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(c_0_18,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)],[fact_irrefl__def]) ).
fof(c_0_19,plain,
! [X151,X152,X153] :
( ( ~ c_member(X153,X152,X151)
| hBOOL(hAPP(X151,X152)) )
& ( ~ hBOOL(hAPP(X151,X152))
| c_member(X153,X152,X151) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
cnf(c_0_20,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,hypothesis,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_0)) )
& ( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_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,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_2])])])]) ).
fof(c_0_23,hypothesis,
! [X2030] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X2030))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X2030))
& 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,X2030)) ),
inference(variable_rename,[status(thm)],[conj_0]) ).
fof(c_0_24,plain,
! [X83,X84,X85,X86,X87] :
( ( ~ c_Relation_Oirrefl(X84,X83)
| ~ c_member(tc_prod(X84,X84),c_Product__Type_OPair(X84,X84,X85,X85),X83) )
& ( c_member(tc_prod(X87,X87),c_Product__Type_OPair(X87,X87,esk2_2(X86,X87),esk2_2(X86,X87)),X86)
| c_Relation_Oirrefl(X87,X86) ) ),
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_18])])])])]) ).
cnf(c_0_25,plain,
( c_member(X3,X2,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( hBOOL(hAPP(X1,X2))
| ~ c_member(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,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_1]) ).
fof(c_0_28,plain,
! [X700,X701] :
( ~ c_Relation_Otrans(X701,X700)
| c_Transitive__Closure_Otrancl(X701,X700) = X700 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).
cnf(c_0_29,hypothesis,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,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_23]) ).
cnf(c_0_33,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_24]) ).
cnf(c_0_34,plain,
c_member(X1,X2,c_Set_Oinsert(X3,X2,X4)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
fof(c_0_35,plain,
! [X704,X705,X706,X707,X708] :
( ~ c_member(tc_prod(X708,X708),c_Product__Type_OPair(X708,X708,X707,X706),X705)
| ~ c_member(tc_prod(X708,X708),c_Product__Type_OPair(X708,X708,X706,X704),X705)
| c_member(tc_prod(X708,X708),c_Product__Type_OPair(X708,X708,X707,X704),c_Transitive__Closure_Otrancl(X708,X705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
cnf(c_0_36,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_26,c_0_27]) ).
cnf(c_0_37,plain,
( c_Transitive__Closure_Otrancl(X1,X2) = X2
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,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_29,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_39,hypothesis,
! [X2033,X2034] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_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,esk88_0))
| X2033 = X2034
| ~ 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,X2033,X2034),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,X2033,X2034),v_F(v_P)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])]) ).
cnf(c_0_40,plain,
~ c_Relation_Oirrefl(X1,c_Set_Oinsert(X2,c_Product__Type_OPair(X1,X1,X3,X3),X4)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,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_35]) ).
cnf(c_0_42,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_25,c_0_36]) ).
cnf(c_0_43,hypothesis,
c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) = v_F(v_P),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,hypothesis,
( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_45,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_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_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,esk88_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)],[c_0_39]) ).
fof(c_0_46,plain,
! [X114,X115] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X115,tc_HOL_Obool)),X114)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(c_0_47,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)],[fact_acyclic__def]) ).
cnf(c_0_48,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_49,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_41,c_0_42]),c_0_43]) ).
cnf(c_0_50,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_44,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_51,plain,
( c_member(X1,X2,X3)
| ~ c_member(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_52,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(rw,[status(thm)],[c_0_45,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_53,plain,
! [X89,X90,X91,X92,X93,X94,X95,X96] :
( ( ~ c_Relation_Ototal__on(X91,X90,X89)
| ~ c_member(X91,X92,X90)
| ~ c_member(X91,X93,X90)
| X92 = X93
| c_member(tc_prod(X91,X91),c_Product__Type_OPair(X91,X91,X92,X93),X89)
| c_member(tc_prod(X91,X91),c_Product__Type_OPair(X91,X91,X93,X92),X89) )
& ( c_member(X96,esk3_3(X94,X95,X96),X95)
| c_Relation_Ototal__on(X96,X95,X94) )
& ( c_member(X96,esk4_3(X94,X95,X96),X95)
| c_Relation_Ototal__on(X96,X95,X94) )
& ( esk3_3(X94,X95,X96) != esk4_3(X94,X95,X96)
| c_Relation_Ototal__on(X96,X95,X94) )
& ( ~ c_member(tc_prod(X96,X96),c_Product__Type_OPair(X96,X96,esk3_3(X94,X95,X96),esk4_3(X94,X95,X96)),X94)
| c_Relation_Ototal__on(X96,X95,X94) )
& ( ~ c_member(tc_prod(X96,X96),c_Product__Type_OPair(X96,X96,esk4_3(X94,X95,X96),esk3_3(X94,X95,X96)),X94)
| c_Relation_Ototal__on(X96,X95,X94) ) ),
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)],[fact_total__on__def])])])])])]) ).
cnf(c_0_54,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_55,plain,
! [X856,X857,X858,X859,X860] :
( ( ~ c_Wellfounded_Oacyclic(X857,X856)
| ~ c_member(tc_prod(X857,X857),c_Product__Type_OPair(X857,X857,X858,X858),c_Transitive__Closure_Otrancl(X857,X856)) )
& ( c_member(tc_prod(X860,X860),c_Product__Type_OPair(X860,X860,esk67_2(X859,X860),esk67_2(X859,X860)),c_Transitive__Closure_Otrancl(X860,X859))
| c_Wellfounded_Oacyclic(X860,X859) ) ),
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_47])])])])]) ).
fof(c_0_56,plain,
! [X154,X155,X156,X157,X158] :
( ( ~ c_FunDef_Oin__rel(X158,X157,X156,X155,X154)
| c_member(tc_prod(X158,X157),c_Product__Type_OPair(X158,X157,X155,X154),X156) )
& ( ~ c_member(tc_prod(X158,X157),c_Product__Type_OPair(X158,X157,X155,X154),X156)
| c_FunDef_Oin__rel(X158,X157,X156,X155,X154) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
cnf(c_0_57,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_48,c_0_49]),c_0_50])]) ).
cnf(c_0_58,hypothesis,
( X1 = X2
| c_member(X3,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(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,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_53]) ).
cnf(c_0_60,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_25,c_0_54]) ).
fof(c_0_61,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])]) ).
cnf(c_0_62,plain,
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,esk67_2(X2,X1),esk67_2(X2,X1)),c_Transitive__Closure_Otrancl(X1,X2))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,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_56]) ).
cnf(c_0_64,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_57,c_0_58]) ).
cnf(c_0_65,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_59,c_0_32]),c_0_60]),c_0_60])]) ).
cnf(c_0_66,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_61]) ).
cnf(c_0_67,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_55]) ).
cnf(c_0_68,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Relation_Oirrefl(X1,c_Transitive__Closure_Otrancl(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_62]) ).
cnf(c_0_69,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_63,c_0_42]) ).
cnf(c_0_70,hypothesis,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_71,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_67,c_0_43]) ).
cnf(c_0_72,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_68,c_0_43]),c_0_50])]) ).
cnf(c_0_73,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_56]) ).
cnf(c_0_74,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_69,c_0_70]) ).
cnf(c_0_75,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_71,c_0_72])]) ).
cnf(c_0_76,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18 % Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% 0.18/0.19 % Command : run_E %s %d THM
% 0.19/0.40 % Computer : n010.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 2400
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Mon Oct 2 11:26:35 EDT 2023
% 0.19/0.40 % CPUTime :
% 0.39/0.63 Running first-order theorem proving
% 0.39/0.63 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.HTs5D4M5KG/E---3.1_10919.p
% 137.35/18.06 # Version: 3.1pre001
% 137.35/18.06 # Preprocessing class: FSLSSMSSSSSNFFN.
% 137.35/18.06 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.35/18.06 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.35/18.06 # Starting new_bool_3 with 300s (1) cores
% 137.35/18.06 # Starting new_bool_1 with 300s (1) cores
% 137.35/18.06 # Starting sh5l with 300s (1) cores
% 137.35/18.06 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 11015 completed with status 0
% 137.35/18.06 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 137.35/18.06 # Preprocessing class: FSLSSMSSSSSNFFN.
% 137.35/18.06 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.35/18.06 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.35/18.06 # No SInE strategy applied
% 137.35/18.06 # Search class: FGHSM-FSLM33-DFFFFFNN
% 137.35/18.06 # Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 137.35/18.06 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S0S with 271s (1) cores
% 137.35/18.06 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 137.35/18.06 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 137.35/18.06 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 137.35/18.06 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 137.35/18.06 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 11026 completed with status 0
% 137.35/18.06 # Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 137.35/18.06 # Preprocessing class: FSLSSMSSSSSNFFN.
% 137.35/18.06 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 137.35/18.06 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 137.35/18.06 # No SInE strategy applied
% 137.35/18.06 # Search class: FGHSM-FSLM33-DFFFFFNN
% 137.35/18.06 # Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 137.35/18.06 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S0S with 271s (1) cores
% 137.35/18.06 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 137.35/18.06 # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 137.35/18.06 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 137.35/18.06 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 137.35/18.06 # Preprocessing time : 0.012 s
% 137.35/18.06 # Presaturation interreduction done
% 137.35/18.06
% 137.35/18.06 # Proof found!
% 137.35/18.06 # SZS status Theorem
% 137.35/18.06 # SZS output start CNFRefutation
% See solution above
% 137.35/18.06 # Parsed axioms : 527
% 137.35/18.06 # Removed by relevancy pruning/SinE : 0
% 137.35/18.06 # Initial clauses : 790
% 137.35/18.06 # Removed in clause preprocessing : 33
% 137.35/18.06 # Initial clauses in saturation : 757
% 137.35/18.06 # Processed clauses : 18841
% 137.35/18.06 # ...of these trivial : 3023
% 137.35/18.06 # ...subsumed : 8847
% 137.35/18.06 # ...remaining for further processing : 6971
% 137.35/18.06 # Other redundant clauses eliminated : 1342
% 137.35/18.06 # Clauses deleted for lack of memory : 0
% 137.35/18.06 # Backward-subsumed : 504
% 137.35/18.06 # Backward-rewritten : 429
% 137.35/18.06 # Generated clauses : 977892
% 137.35/18.06 # ...of the previous two non-redundant : 876046
% 137.35/18.06 # ...aggressively subsumed : 0
% 137.35/18.06 # Contextual simplify-reflections : 10
% 137.35/18.06 # Paramodulations : 976544
% 137.35/18.06 # Factorizations : 2
% 137.35/18.06 # NegExts : 0
% 137.35/18.06 # Equation resolutions : 1357
% 137.35/18.06 # Total rewrite steps : 233411
% 137.35/18.06 # Propositional unsat checks : 0
% 137.35/18.06 # Propositional check models : 0
% 137.35/18.06 # Propositional check unsatisfiable : 0
% 137.35/18.06 # Propositional clauses : 0
% 137.35/18.06 # Propositional clauses after purity: 0
% 137.35/18.06 # Propositional unsat core size : 0
% 137.35/18.06 # Propositional preprocessing time : 0.000
% 137.35/18.06 # Propositional encoding time : 0.000
% 137.35/18.06 # Propositional solver time : 0.000
% 137.35/18.06 # Success case prop preproc time : 0.000
% 137.35/18.06 # Success case prop encoding time : 0.000
% 137.35/18.06 # Success case prop solver time : 0.000
% 137.35/18.06 # Current number of processed clauses : 5359
% 137.35/18.06 # Positive orientable unit clauses : 2952
% 137.35/18.06 # Positive unorientable unit clauses: 11
% 137.35/18.06 # Negative unit clauses : 278
% 137.35/18.06 # Non-unit-clauses : 2118
% 137.35/18.06 # Current number of unprocessed clauses: 841338
% 137.35/18.06 # ...number of literals in the above : 1812129
% 137.35/18.06 # Current number of archived formulas : 0
% 137.35/18.06 # Current number of archived clauses : 1547
% 137.35/18.06 # Clause-clause subsumption calls (NU) : 857518
% 137.35/18.06 # Rec. Clause-clause subsumption calls : 523634
% 137.35/18.06 # Non-unit clause-clause subsumptions : 5399
% 137.35/18.06 # Unit Clause-clause subsumption calls : 76064
% 137.35/18.06 # Rewrite failures with RHS unbound : 307
% 137.35/18.06 # BW rewrite match attempts : 633558
% 137.35/18.06 # BW rewrite match successes : 529
% 137.35/18.06 # Condensation attempts : 0
% 137.35/18.06 # Condensation successes : 0
% 137.35/18.06 # Termbank termtop insertions : 15849352
% 137.35/18.06
% 137.35/18.06 # -------------------------------------------------
% 137.35/18.06 # User time : 16.468 s
% 137.35/18.06 # System time : 0.585 s
% 137.35/18.06 # Total time : 17.053 s
% 137.35/18.06 # Maximum resident set size: 5368 pages
% 137.35/18.06
% 137.35/18.06 # -------------------------------------------------
% 137.35/18.06 # User time : 82.605 s
% 137.35/18.06 # System time : 2.263 s
% 137.35/18.06 # Total time : 84.868 s
% 137.35/18.06 # Maximum resident set size: 2404 pages
% 137.35/18.06 % E---3.1 exiting
% 137.35/18.07 % E---3.1 exiting
%------------------------------------------------------------------------------