TSTP Solution File: SWW363+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWW363+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 20:09:13 EDT 2023
% Result : ContradictoryAxioms 59.44s 10.15s
% Output : CNFRefutation 59.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 83 ( 63 unt; 0 def)
% Number of atoms : 117 ( 48 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 66 ( 32 ~; 22 |; 5 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 6 con; 0-3 aty)
% Number of variables : 137 ( 22 sgn; 73 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_number__of__is__id,axiom,
! [X24] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24) = X24,
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_number__of__is__id) ).
fof(fact_nat__number__of__def,axiom,
! [X90] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_nat__number__of__def) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_one__is__num__one) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_Pls__def) ).
fof(fact_card__infinite,axiom,
! [X11,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X11))
=> hAPP(c_Finite__Set_Ocard(X10),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_card__infinite) ).
fof(fact_card__UNIV__bool,axiom,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_card__UNIV__bool) ).
fof(fact_semiring__norm_I115_J,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_semiring__norm_I115_J) ).
fof(fact_Zero__not__Suc,axiom,
! [X16] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X16),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_Zero__not__Suc) ).
fof(fact_finite__Un,axiom,
! [X4,X9,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X9),X4)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X4)) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_finite__Un) ).
fof(fact_Un__UNIV__right,axiom,
! [X11,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X11),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_Un__UNIV__right) ).
fof(fact_Collect__mem__eq,axiom,
! [X11,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X11)) = X11,
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X44,X10] : hAPP(c_Set_OCollect(X10),X44) = X44,
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_Collect__def) ).
fof(fact_finite__UnionD,axiom,
! [X11,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X11)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),X11)) ),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_finite__UnionD) ).
fof(fact_less__not__refl,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17)),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_less__not__refl) ).
fof(help_c__COMBC__1,axiom,
! [X43,X50,X44,X10,X27,X8] : hAPP(hAPP(hAPP(c_COMBC(X8,X27,X10),X44),X50),X43) = hAPP(hAPP(X44,X43),X50),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',help_c__COMBC__1) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X33] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X33)),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_less__eq__Suc__le__raw) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X48] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X48))
<=> ? [X67] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X48))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X67)) ) ),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_rangeI,axiom,
! [X8,X14,X2,X10] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X14)),hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))))),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_rangeI) ).
fof(fact_finite__imageI,axiom,
! [X7,X8,X9,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_Oimage(X10,X8,X7),X9))) ),
file('/export/starexec/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p',fact_finite__imageI) ).
fof(c_0_20,plain,
! [X3340] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X3340) = X3340,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(c_0_21,plain,
! [X2825] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2825) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2825)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
cnf(c_0_22,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).
cnf(c_0_23,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_26,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_27,plain,
! [X11,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X11))
=> hAPP(c_Finite__Set_Ocard(X10),X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
cnf(c_0_28,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool]) ).
cnf(c_0_29,plain,
c_Int_OBit1(c_Int_OPls) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X1),
inference(rw,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_31,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
cnf(c_0_32,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_33,plain,
! [X749,X750] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X750),X749))
| hAPP(c_Finite__Set_Ocard(X750),X749) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
fof(c_0_34,plain,
! [X1336] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1336),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_35,plain,
! [X1696,X1697,X1698] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1698),X1697))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1698),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1698,tc_HOL_Obool)),X1697),X1696))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1698),X1696))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1698),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1698,tc_HOL_Obool)),X1697),X1696))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1698),X1697))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1698),X1696))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1698),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1698,tc_HOL_Obool)),X1697),X1696))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])]) ).
fof(c_0_36,plain,
! [X1908,X1909] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1909,tc_HOL_Obool)),X1908),c_Orderings_Otop__class_Otop(tc_fun(X1909,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1909,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Un__UNIV__right]) ).
cnf(c_0_37,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onat,c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_38,plain,
hAPP(c_Int_Onat,c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29]),c_0_30]),c_0_32]) ).
cnf(c_0_39,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(c_Int_Onat,c_Int_OPls)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(rw,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_45,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_40,c_0_32]) ).
fof(c_0_46,plain,
! [X3574,X3575] : hAPP(c_Set_OCollect(X3575),hAPP(hAPP(c_COMBC(X3575,tc_fun(X3575,tc_HOL_Obool),tc_HOL_Obool),c_member(X3575)),X3574)) = X3574,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_47,plain,
! [X3560,X3561] : hAPP(c_Set_OCollect(X3561),X3560) = X3560,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_48,plain,
! [X6030,X6031] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X6031),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6031,tc_HOL_Obool),X6030)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X6031,tc_HOL_Obool)),X6030)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])]) ).
cnf(c_0_49,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
fof(c_0_51,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(c_0_52,plain,
! [X3501,X3502,X3503,X3504,X3505,X3506] : hAPP(hAPP(hAPP(c_COMBC(X3506,X3505,X3504),X3503),X3502),X3501) = hAPP(hAPP(X3503,X3501),X3502),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_53,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),X1)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_57,plain,
! [X1408] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1408),X1408)),
inference(variable_rename,[status(thm)],[c_0_51]) ).
fof(c_0_58,plain,
! [X1324] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1324) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1324)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_59,plain,
! [X334,X336,X337,X338] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X334))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X336),X334))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X336),esk11_1(X334))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk12_2(X337,X338)),X337))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X337)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk12_2(X337,X338)),X338))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X337)) ) ),
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_finite__nat__set__iff__bounded__le])])])])])]) ).
cnf(c_0_60,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk11_1(X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_67,plain,
! [X660,X661,X662,X663] : hBOOL(hAPP(hAPP(c_member(X663),hAPP(X662,X661)),hAPP(c_Set_Oimage(X660,X663,X662),c_Orderings_Otop__class_Otop(tc_fun(X660,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_68,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_HOL_Obool)),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_62]) ).
cnf(c_0_69,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk11_1(X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_72,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(tc_fun(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool)),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_68]) ).
cnf(c_0_73,plain,
( ~ hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk11_1(X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(X3,X4))),
inference(rw,[status(thm)],[c_0_71,c_0_66]) ).
fof(c_0_75,plain,
! [X563,X564,X565,X566] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X566),X565))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X564),hAPP(c_Set_Oimage(X566,X564,X563),X565))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
cnf(c_0_76,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(tc_fun(tc_fun(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool)),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_72]) ).
cnf(c_0_77,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(X1,X2,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_79,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(tc_fun(tc_fun(tc_fun(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool)),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_76]) ).
cnf(c_0_80,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(tc_fun(tc_fun(tc_fun(tc_fun(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool)),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_79]) ).
cnf(c_0_82,plain,
$false,
inference(spm,[status(thm)],[c_0_80,c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.83/0.87 % Problem : SWW363+1 : TPTP v8.1.2. Released v5.2.0.
% 0.83/0.88 % Command : run_E %s %d THM
% 0.92/1.10 % Computer : n027.cluster.edu
% 0.92/1.10 % Model : x86_64 x86_64
% 0.92/1.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.92/1.10 % Memory : 8042.1875MB
% 0.92/1.10 % OS : Linux 3.10.0-693.el7.x86_64
% 0.92/1.10 % CPULimit : 2400
% 0.92/1.10 % WCLimit : 300
% 0.92/1.10 % DateTime : Mon Oct 2 22:54:46 EDT 2023
% 0.92/1.10 % CPUTime :
% 1.78/1.95 Running first-order theorem proving
% 1.78/1.95 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.PwHrCveQhG/E---3.1_31578.p
% 59.44/10.15 # Version: 3.1pre001
% 59.44/10.15 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.44/10.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.44/10.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.44/10.15 # Starting new_bool_3 with 300s (1) cores
% 59.44/10.15 # Starting new_bool_1 with 300s (1) cores
% 59.44/10.15 # Starting sh5l with 300s (1) cores
% 59.44/10.15 # new_bool_3 with pid 31657 completed with status 0
% 59.44/10.15 # Result found by new_bool_3
% 59.44/10.15 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.44/10.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.44/10.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.44/10.15 # Starting new_bool_3 with 300s (1) cores
% 59.44/10.15 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 59.44/10.15 # Search class: FGHSM-SMLM33-DFFFFFNN
% 59.44/10.15 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 59.44/10.15 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 59.44/10.15 # SAT001_MinMin_p005000_rr with pid 31661 completed with status 0
% 59.44/10.15 # Result found by SAT001_MinMin_p005000_rr
% 59.44/10.15 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.44/10.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.44/10.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.44/10.15 # Starting new_bool_3 with 300s (1) cores
% 59.44/10.15 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 59.44/10.15 # Search class: FGHSM-SMLM33-DFFFFFNN
% 59.44/10.15 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 59.44/10.15 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 59.44/10.15 # Preprocessing time : 0.044 s
% 59.44/10.15 # Presaturation interreduction done
% 59.44/10.15
% 59.44/10.15 # Proof found!
% 59.44/10.15 # SZS status ContradictoryAxioms
% 59.44/10.15 # SZS output start CNFRefutation
% See solution above
% 59.44/10.15 # Parsed axioms : 5229
% 59.44/10.15 # Removed by relevancy pruning/SinE : 3441
% 59.44/10.15 # Initial clauses : 2715
% 59.44/10.15 # Removed in clause preprocessing : 70
% 59.44/10.15 # Initial clauses in saturation : 2645
% 59.44/10.15 # Processed clauses : 16863
% 59.44/10.15 # ...of these trivial : 326
% 59.44/10.15 # ...subsumed : 9208
% 59.44/10.15 # ...remaining for further processing : 7329
% 59.44/10.15 # Other redundant clauses eliminated : 5722
% 59.44/10.15 # Clauses deleted for lack of memory : 0
% 59.44/10.15 # Backward-subsumed : 422
% 59.44/10.15 # Backward-rewritten : 228
% 59.44/10.15 # Generated clauses : 431411
% 59.44/10.15 # ...of the previous two non-redundant : 414826
% 59.44/10.15 # ...aggressively subsumed : 0
% 59.44/10.15 # Contextual simplify-reflections : 29
% 59.44/10.15 # Paramodulations : 425606
% 59.44/10.15 # Factorizations : 22
% 59.44/10.15 # NegExts : 0
% 59.44/10.15 # Equation resolutions : 5804
% 59.44/10.15 # Total rewrite steps : 41602
% 59.44/10.15 # Propositional unsat checks : 1
% 59.44/10.15 # Propositional check models : 0
% 59.44/10.15 # Propositional check unsatisfiable : 0
% 59.44/10.15 # Propositional clauses : 0
% 59.44/10.15 # Propositional clauses after purity: 0
% 59.44/10.15 # Propositional unsat core size : 0
% 59.44/10.15 # Propositional preprocessing time : 0.000
% 59.44/10.15 # Propositional encoding time : 0.260
% 59.44/10.15 # Propositional solver time : 0.089
% 59.44/10.15 # Success case prop preproc time : 0.000
% 59.44/10.15 # Success case prop encoding time : 0.000
% 59.44/10.15 # Success case prop solver time : 0.000
% 59.44/10.15 # Current number of processed clauses : 4493
% 59.44/10.15 # Positive orientable unit clauses : 595
% 59.44/10.15 # Positive unorientable unit clauses: 47
% 59.44/10.15 # Negative unit clauses : 440
% 59.44/10.15 # Non-unit-clauses : 3411
% 59.44/10.15 # Current number of unprocessed clauses: 376199
% 59.44/10.15 # ...number of literals in the above : 1155300
% 59.44/10.15 # Current number of archived formulas : 0
% 59.44/10.15 # Current number of archived clauses : 2630
% 59.44/10.15 # Clause-clause subsumption calls (NU) : 2129553
% 59.44/10.15 # Rec. Clause-clause subsumption calls : 1215943
% 59.44/10.15 # Non-unit clause-clause subsumptions : 7534
% 59.44/10.15 # Unit Clause-clause subsumption calls : 57734
% 59.44/10.15 # Rewrite failures with RHS unbound : 215
% 59.44/10.15 # BW rewrite match attempts : 12391
% 59.44/10.15 # BW rewrite match successes : 684
% 59.44/10.15 # Condensation attempts : 0
% 59.44/10.15 # Condensation successes : 0
% 59.44/10.15 # Termbank termtop insertions : 10380189
% 59.44/10.15
% 59.44/10.15 # -------------------------------------------------
% 59.44/10.15 # User time : 7.618 s
% 59.44/10.15 # System time : 0.289 s
% 59.44/10.15 # Total time : 7.907 s
% 59.44/10.15 # Maximum resident set size: 17324 pages
% 59.44/10.15
% 59.44/10.15 # -------------------------------------------------
% 59.44/10.15 # User time : 7.754 s
% 59.44/10.15 # System time : 0.297 s
% 59.44/10.15 # Total time : 8.050 s
% 59.44/10.15 # Maximum resident set size: 9464 pages
% 59.44/10.15 % E---3.1 exiting
% 59.44/10.15 % E---3.1 exiting
%------------------------------------------------------------------------------