TSTP Solution File: SWW324+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SWW324+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 20:11:02 EDT 2023
% Result : ContradictoryAxioms 28.01s 5.90s
% Output : CNFRefutation 28.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 73 ( 56 unt; 0 def)
% Number of atoms : 104 ( 47 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 61 ( 30 ~; 20 |; 5 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 125 ( 16 sgn; 69 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__mem__eq,axiom,
! [X17,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X17)) = X17,
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X13,X10] : hAPP(c_Set_OCollect(X10),X13) = X13,
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_Collect__def) ).
fof(fact_less__not__refl,axiom,
! [X111] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X111),X111)),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_less__not__refl) ).
fof(help_c__COMBC__1,axiom,
! [X43,X23,X13,X10,X26,X16] : hAPP(hAPP(hAPP(c_COMBC(X16,X26,X10),X13),X23),X43) = hAPP(hAPP(X13,X43),X23),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',help_c__COMBC__1) ).
fof(fact_number__of__is__id,axiom,
! [X113] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X113) = X113,
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_number__of__is__id) ).
fof(fact_nat__number__of__def,axiom,
! [X132] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X132) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X132)),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_nat__number__of__def) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X93] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X93) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X93)),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_less__eq__Suc__le__raw) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X105] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X105))
<=> ? [X106] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X105))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X106)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_finite__nat__set__iff__bounded__le) ).
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/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_one__is__num__one) ).
fof(fact_card__infinite,axiom,
! [X17,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X17))
=> hAPP(c_Finite__Set_Ocard(X10),X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_card__infinite) ).
fof(fact_rangeI,axiom,
! [X16,X20,X2,X10] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X20)),hAPP(c_Set_Oimage(X16,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X16,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_rangeI) ).
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/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_card__UNIV__bool) ).
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/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.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/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_Pls__def) ).
fof(fact_Zero__neq__Suc,axiom,
! [X112] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X112),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_Zero__neq__Suc) ).
fof(fact_finite__Un,axiom,
! [X14,X91,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X91),X14)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X91))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X14)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_finite__Un) ).
fof(fact_Un__UNIV__left,axiom,
! [X67,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X67) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_Un__UNIV__left) ).
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/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_semiring__norm_I115_J) ).
fof(fact_finite__imageI,axiom,
! [X24,X16,X91,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X91))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X16),hAPP(c_Set_Oimage(X10,X16,X24),X91))) ),
file('/export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p',fact_finite__imageI) ).
fof(c_0_19,plain,
! [X3207,X3208] : hAPP(c_Set_OCollect(X3208),hAPP(hAPP(c_COMBC(X3208,tc_fun(X3208,tc_HOL_Obool),tc_HOL_Obool),c_member(X3208)),X3207)) = X3207,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_20,plain,
! [X3218,X3219] : hAPP(c_Set_OCollect(X3219),X3218) = X3218,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X111] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X111),X111)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(c_0_22,plain,
! [X3133,X3134,X3135,X3136,X3137,X3138] : hAPP(hAPP(hAPP(c_COMBC(X3138,X3137,X3136),X3135),X3134),X3133) = hAPP(hAPP(X3135,X3133),X3134),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_23,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_19]) ).
cnf(c_0_24,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X3849] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X3849) = X3849,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(c_0_26,plain,
! [X5057] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5057) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5057)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
fof(c_0_27,plain,
! [X1342] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1342),X1342)),
inference(variable_rename,[status(thm)],[c_0_21]) ).
fof(c_0_28,plain,
! [X3715] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3715) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3715)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_29,plain,
! [X1477,X1479,X1480,X1481] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1477))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1479),X1477))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1479),esk33_1(X1477))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk34_2(X1480,X1481)),X1480))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1480)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk34_2(X1480,X1481)),X1481))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1480)) ) ),
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_30,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,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_23,c_0_24]) ).
cnf(c_0_32,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_33,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,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_26]) ).
fof(c_0_35,plain,
! [X17,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X17))
=> hAPP(c_Finite__Set_Ocard(X10),X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
cnf(c_0_36,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,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_28]) ).
cnf(c_0_38,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk33_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_29]) ).
cnf(c_0_39,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_40,plain,
! [X2222,X2223,X2224,X2225] : hBOOL(hAPP(hAPP(c_member(X2225),hAPP(X2224,X2223)),hAPP(c_Set_Oimage(X2222,X2225,X2224),c_Orderings_Otop__class_Otop(tc_fun(X2222,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_41,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_42,plain,
c_Int_OBit1(c_Int_OPls) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X1),
inference(rw,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_44,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_45,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_46,plain,
! [X4253,X4254] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4254),X4253))
| hAPP(c_Finite__Set_Ocard(X4254),X4253) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])]) ).
fof(c_0_47,plain,
! [X3740] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3740),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
cnf(c_0_48,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_36,c_0_37]) ).
cnf(c_0_49,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk33_1(X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,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_40]) ).
fof(c_0_51,plain,
! [X1492,X1493,X1494] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1494),X1493))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1494),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1494,tc_HOL_Obool)),X1493),X1492))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1494),X1492))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1494),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1494,tc_HOL_Obool)),X1493),X1492))) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1494),X1493))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1494),X1492))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1494),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1494,tc_HOL_Obool)),X1493),X1492))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])]) ).
fof(c_0_52,plain,
! [X3052,X3053] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3053,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3053,tc_HOL_Obool))),X3052) = c_Orderings_Otop__class_Otop(tc_fun(X3053,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Un__UNIV__left]) ).
cnf(c_0_53,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_54,plain,
hAPP(c_Int_Onat,c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_55,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_56,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_46]) ).
cnf(c_0_57,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,plain,
( ~ hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk33_1(X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,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_50,c_0_39]) ).
fof(c_0_60,plain,
! [X2203,X2204,X2205,X2206] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2206),X2205))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X2204),hAPP(c_Set_Oimage(X2206,X2204,X2203),X2205))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
cnf(c_0_61,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)),X3),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_42]),c_0_43]),c_0_54]),c_0_55]) ).
cnf(c_0_64,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_56,c_0_55]) ).
cnf(c_0_65,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_57,c_0_55]) ).
cnf(c_0_66,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_58,c_0_59]) ).
cnf(c_0_67,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_60]) ).
cnf(c_0_68,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_61,c_0_62]) ).
cnf(c_0_69,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_63,c_0_64]),c_0_65]) ).
cnf(c_0_70,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_66,c_0_67]) ).
cnf(c_0_71,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),X1)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,plain,
$false,
inference(spm,[status(thm)],[c_0_70,c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWW324+1 : TPTP v8.1.2. Released v5.2.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n005.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 2400
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Oct 2 22:04:31 EDT 2023
% 0.11/0.32 % CPUTime :
% 1.30/1.51 Running first-order model finding
% 1.30/1.51 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.FO3bK4iqD4/E---3.1_18416.p
% 28.01/5.90 # Version: 3.1pre001
% 28.01/5.90 # Preprocessing class: FMLMSMSMSSSNFFN.
% 28.01/5.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.01/5.90 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 28.01/5.90 # Starting new_bool_3 with 300s (1) cores
% 28.01/5.90 # Starting new_bool_1 with 300s (1) cores
% 28.01/5.90 # Starting sh5l with 300s (1) cores
% 28.01/5.90 # new_bool_3 with pid 18494 completed with status 0
% 28.01/5.90 # Result found by new_bool_3
% 28.01/5.90 # Preprocessing class: FMLMSMSMSSSNFFN.
% 28.01/5.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.01/5.90 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 28.01/5.90 # Starting new_bool_3 with 300s (1) cores
% 28.01/5.90 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 28.01/5.90 # Search class: FGHSM-SMLM33-DFFFFFNN
% 28.01/5.90 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 28.01/5.90 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 28.01/5.90 # SAT001_MinMin_p005000_rr with pid 18497 completed with status 0
% 28.01/5.90 # Result found by SAT001_MinMin_p005000_rr
% 28.01/5.90 # Preprocessing class: FMLMSMSMSSSNFFN.
% 28.01/5.90 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.01/5.90 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 28.01/5.90 # Starting new_bool_3 with 300s (1) cores
% 28.01/5.90 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 28.01/5.90 # Search class: FGHSM-SMLM33-DFFFFFNN
% 28.01/5.90 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 28.01/5.90 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 28.01/5.90 # Preprocessing time : 0.064 s
% 28.01/5.90 # Presaturation interreduction done
% 28.01/5.90
% 28.01/5.90 # Proof found!
% 28.01/5.90 # SZS status ContradictoryAxioms
% 28.01/5.90 # SZS output start CNFRefutation
% See solution above
% 28.01/5.90 # Parsed axioms : 5230
% 28.01/5.90 # Removed by relevancy pruning/SinE : 3314
% 28.01/5.90 # Initial clauses : 2925
% 28.01/5.90 # Removed in clause preprocessing : 80
% 28.01/5.90 # Initial clauses in saturation : 2845
% 28.01/5.90 # Processed clauses : 10913
% 28.01/5.90 # ...of these trivial : 494
% 28.01/5.90 # ...subsumed : 4441
% 28.01/5.90 # ...remaining for further processing : 5978
% 28.01/5.90 # Other redundant clauses eliminated : 596
% 28.01/5.90 # Clauses deleted for lack of memory : 0
% 28.01/5.90 # Backward-subsumed : 72
% 28.01/5.90 # Backward-rewritten : 398
% 28.01/5.90 # Generated clauses : 127589
% 28.01/5.90 # ...of the previous two non-redundant : 120899
% 28.01/5.90 # ...aggressively subsumed : 0
% 28.01/5.90 # Contextual simplify-reflections : 19
% 28.01/5.90 # Paramodulations : 126977
% 28.01/5.90 # Factorizations : 12
% 28.01/5.90 # NegExts : 0
% 28.01/5.90 # Equation resolutions : 637
% 28.01/5.90 # Total rewrite steps : 27827
% 28.01/5.90 # Propositional unsat checks : 1
% 28.01/5.90 # Propositional check models : 0
% 28.01/5.90 # Propositional check unsatisfiable : 0
% 28.01/5.90 # Propositional clauses : 0
% 28.01/5.90 # Propositional clauses after purity: 0
% 28.01/5.90 # Propositional unsat core size : 0
% 28.01/5.90 # Propositional preprocessing time : 0.000
% 28.01/5.90 # Propositional encoding time : 0.166
% 28.01/5.90 # Propositional solver time : 0.067
% 28.01/5.90 # Success case prop preproc time : 0.000
% 28.01/5.90 # Success case prop encoding time : 0.000
% 28.01/5.90 # Success case prop solver time : 0.000
% 28.01/5.90 # Current number of processed clauses : 3139
% 28.01/5.90 # Positive orientable unit clauses : 720
% 28.01/5.90 # Positive unorientable unit clauses: 57
% 28.01/5.90 # Negative unit clauses : 507
% 28.01/5.90 # Non-unit-clauses : 1855
% 28.01/5.90 # Current number of unprocessed clauses: 97590
% 28.01/5.90 # ...number of literals in the above : 207835
% 28.01/5.90 # Current number of archived formulas : 0
% 28.01/5.90 # Current number of archived clauses : 2612
% 28.01/5.90 # Clause-clause subsumption calls (NU) : 845671
% 28.01/5.90 # Rec. Clause-clause subsumption calls : 507120
% 28.01/5.90 # Non-unit clause-clause subsumptions : 2406
% 28.01/5.90 # Unit Clause-clause subsumption calls : 61781
% 28.01/5.90 # Rewrite failures with RHS unbound : 458
% 28.01/5.90 # BW rewrite match attempts : 13492
% 28.01/5.90 # BW rewrite match successes : 981
% 28.01/5.90 # Condensation attempts : 0
% 28.01/5.90 # Condensation successes : 0
% 28.01/5.90 # Termbank termtop insertions : 3462617
% 28.01/5.90
% 28.01/5.90 # -------------------------------------------------
% 28.01/5.90 # User time : 3.913 s
% 28.01/5.90 # System time : 0.141 s
% 28.01/5.90 # Total time : 4.054 s
% 28.01/5.90 # Maximum resident set size: 17920 pages
% 28.01/5.90
% 28.01/5.90 # -------------------------------------------------
% 28.01/5.90 # User time : 4.160 s
% 28.01/5.90 # System time : 0.152 s
% 28.01/5.90 # Total time : 4.313 s
% 28.01/5.90 # Maximum resident set size: 9496 pages
% 28.01/5.90 % E---3.1 exiting
%------------------------------------------------------------------------------