TSTP Solution File: SWW372+1 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SWW372+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:11:47 EDT 2024
% Result : ContradictoryAxioms 142.39s 20.53s
% Output : CNFRefutation 142.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 32
% Syntax : Number of formulae : 128 ( 94 unt; 0 def)
% Number of atoms : 186 ( 94 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 113 ( 55 ~; 42 |; 5 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 37 ( 37 usr; 10 con; 0-3 aty)
% Number of variables : 222 ( 17 sgn 122 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X19,X5] :
( hAPP(c_Set_OCollect(X5),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_Collect__empty__eq) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X16,X17,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X16))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X17))
| X17 = X16 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_Collect__mem__eq,axiom,
! [X10,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X10)) = X10,
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X19,X5] : hAPP(c_Set_OCollect(X5),X19) = X19,
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X19,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X19)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X19)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X19,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(c_Set_OCollect(X20),X19)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X20,tc_HOL_Obool,X5),X19),X2)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_vimage__Collect__eq) ).
fof(help_c__fconj__2,axiom,
! [X18,X19] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X19),X18))
| hBOOL(X19) ),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',help_c__fconj__2) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X90] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X90) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X90)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_less__eq__Suc__le__raw) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X113] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X113))
<=> ? [X143] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X113))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X143)) ) ),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_finite__nat__set__iff__bounded) ).
fof(help_c__COMBC__1,axiom,
! [X49,X18,X19,X5,X82,X20] : hAPP(hAPP(hAPP(c_COMBC(X20,X82,X5),X19),X18),X49) = hAPP(hAPP(X19,X49),X18),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',help_c__COMBC__1) ).
fof(fact_double__complement,axiom,
! [X10,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X10)) = X10,
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_double__complement) ).
fof(fact_vimage__id,axiom,
! [X10,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X10) = X10,
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_vimage__id) ).
fof(help_c__fNot__1,axiom,
! [X19] :
( ~ hBOOL(hAPP(c_fNot,X19))
| ~ hBOOL(X19) ),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',help_c__fNot__1) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(fact_le__refl,axiom,
! [X108] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X108),X108)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_le__refl) ).
fof(fact_number__of__is__id,axiom,
! [X110] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X110) = X110,
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_number__of__is__id) ).
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.p5LxNViyJ1/E---3.1_23358.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.p5LxNViyJ1/E---3.1_23358.p',fact_Pls__def) ).
fof(fact_nat__number__of__def,axiom,
! [X155] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X155) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X155)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_nat__number__of__def) ).
fof(fact_rangeI,axiom,
! [X20,X17,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X17)),hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))))),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_rangeI) ).
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.p5LxNViyJ1/E---3.1_23358.p',fact_one__is__num__one) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_One__nat__def) ).
fof(fact_Compl__partition,axiom,
! [X10,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X10)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_Compl__partition) ).
fof(fact_Compl__Diff__eq,axiom,
! [X12,X10,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X10),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X10)),X12),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_Compl__Diff__eq) ).
fof(fact_neg__number__of__Min,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_neg__number__of__Min) ).
fof(fact_card__infinite,axiom,
! [X10,X5] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X10))
=> hAPP(c_Finite__Set_Ocard(X5),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.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.p5LxNViyJ1/E---3.1_23358.p',fact_card__UNIV__bool) ).
fof(fact_Diff__cancel,axiom,
! [X10,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X10),X10) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_Diff__cancel) ).
fof(fact_Zero__not__Suc,axiom,
! [X109] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X109),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_Zero__not__Suc) ).
fof(fact_finite__imageI,axiom,
! [X101,X20,X78,X5] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X78))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_Oimage(X5,X20,X101),X78))) ),
file('/export/starexec/sandbox/tmp/tmp.p5LxNViyJ1/E---3.1_23358.p',fact_finite__imageI) ).
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.p5LxNViyJ1/E---3.1_23358.p',fact_semiring__norm_I115_J) ).
fof(c_0_32,plain,
! [X19,X5] :
( hAPP(c_Set_OCollect(X5),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_33,plain,
! [X16,X17,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X16))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X17))
| X17 = X16 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(c_0_34,plain,
! [X3623,X3624] : hAPP(c_Set_OCollect(X3624),hAPP(hAPP(c_COMBC(X3624,tc_fun(X3624,tc_HOL_Obool),tc_HOL_Obool),c_member(X3624)),X3623)) = X3623,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_35,plain,
! [X3634,X3635] : hAPP(c_Set_OCollect(X3635),X3634) = X3634,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_36,plain,
! [X1825,X1826] : hAPP(c_Set_OCollect(X1826),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1826),c_fNot),X1825)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1826,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1826),X1825)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_37,plain,
! [X6995,X6996,X6997,X6998] : hAPP(c_Set_Ovimage(X6998,X6997,X6996),hAPP(c_Set_OCollect(X6997),X6995)) = hAPP(c_Set_OCollect(X6998),hAPP(hAPP(c_COMBB(X6997,tc_HOL_Obool,X6998),X6995),X6996)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_38,plain,
! [X18,X19] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X19),X18))
| hBOOL(X19) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(c_0_39,plain,
! [X3611,X3612,X3613,X3614,X3616] :
( ( hAPP(c_Set_OCollect(X3612),X3611) != c_Orderings_Obot__class_Obot(tc_fun(X3612,tc_HOL_Obool))
| ~ hBOOL(hAPP(X3611,X3613)) )
& ( hBOOL(hAPP(X3614,esk83_1(X3614)))
| hAPP(c_Set_OCollect(X3616),X3614) = c_Orderings_Obot__class_Obot(tc_fun(X3616,tc_HOL_Obool)) ) ),
inference(fof_nnf,[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_32])])])])])]) ).
fof(c_0_40,plain,
! [X7560,X7561,X7562] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7562),X7561),X7560))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7562),X7560),X7561))
| X7561 = X7560
| ~ class_Orderings_Olinorder(X7562) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7562),X7560),X7561))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7562),X7561),X7560))
| ~ class_Orderings_Olinorder(X7562) )
& ( X7561 != X7560
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7562),X7561),X7560))
| ~ class_Orderings_Olinorder(X7562) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
fof(c_0_41,plain,
! [X4033] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4033) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4033)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_42,plain,
! [X2076,X2078,X2079,X2080] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2076))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2078),X2076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2078),esk48_1(X2076))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk49_2(X2079,X2080)),X2079))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2079)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk49_2(X2079,X2080)),X2080))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2079)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).
fof(c_0_43,plain,
! [X1123,X1124,X1125,X1126,X1127,X1128] : hAPP(hAPP(hAPP(c_COMBC(X1128,X1127,X1126),X1125),X1124),X1123) = hAPP(hAPP(X1125,X1123),X1124),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_44,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_34]) ).
cnf(c_0_45,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_46,plain,
! [X4632,X4633] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4633,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4633,tc_HOL_Obool)),X4632)) = X4632,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_47,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_48,plain,
! [X7009,X7010] : hAPP(c_Set_Ovimage(X7010,X7010,c_Fun_Oid(X7010)),X7009) = X7009,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
cnf(c_0_49,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_50,plain,
! [X19] :
( ~ hBOOL(hAPP(c_fNot,X19))
| ~ hBOOL(X19) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_51,plain,
! [X1915,X1916] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X1916),X1915))
| hBOOL(X1916) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_38])]) ).
cnf(c_0_52,plain,
( hBOOL(hAPP(X1,esk83_1(X1)))
| hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_53,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,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_41]) ).
cnf(c_0_55,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(c_0_56,plain,
! [X1793] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1793),X1793)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
cnf(c_0_57,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk48_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_42]) ).
cnf(c_0_58,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_59,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_44,c_0_45]) ).
fof(c_0_60,plain,
! [X4481] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4481) = X4481,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
cnf(c_0_61,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_62,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_63,plain,
! [X4370] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4370) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4370)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
cnf(c_0_64,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_65,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_45]),c_0_45]) ).
cnf(c_0_66,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_67,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_45]),c_0_45]) ).
fof(c_0_68,plain,
! [X1846] :
( ~ hBOOL(hAPP(c_fNot,X1846))
| ~ hBOOL(X1846) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_50])]) ).
cnf(c_0_69,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_70,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk83_1(X1))) ),
inference(rw,[status(thm)],[c_0_52,c_0_45]) ).
cnf(c_0_71,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_54])]) ).
cnf(c_0_72,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_73,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),esk48_1(X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)) ),
inference(rw,[status(thm)],[c_0_57,c_0_54]) ).
cnf(c_0_74,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_75,plain,
! [X1957,X1958,X1959,X1960] : hBOOL(hAPP(hAPP(c_member(X1960),hAPP(X1959,X1958)),hAPP(c_Set_Oimage(X1957,X1960,X1959),c_Orderings_Otop__class_Otop(tc_fun(X1957,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_76,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_77,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_78,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]) ).
cnf(c_0_79,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
cnf(c_0_80,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_81,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_63]) ).
fof(c_0_82,plain,
! [X3069,X3070] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3070,tc_HOL_Obool)),X3069),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3070,tc_HOL_Obool)),X3069)) = c_Orderings_Otop__class_Otop(tc_fun(X3070,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__partition]) ).
cnf(c_0_83,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_65]) ).
cnf(c_0_84,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
fof(c_0_85,plain,
! [X2685,X2686,X2687] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2687,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2687,tc_HOL_Obool)),X2686),X2685)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2687,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2687,tc_HOL_Obool)),X2686)),X2685),
inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq]) ).
cnf(c_0_86,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_87,plain,
( hAPP(c_fconj,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_88,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(split_conjunct,[status(thm)],[fact_neg__number__of__Min]) ).
cnf(c_0_89,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X1)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_90,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),esk48_1(X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_91,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_75]) ).
fof(c_0_92,plain,
! [X10,X5] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X10))
=> hAPP(c_Finite__Set_Ocard(X5),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
cnf(c_0_93,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_94,plain,
c_Int_OBit1(c_Int_OPls) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(rw,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_95,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_96,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X1),
inference(rw,[status(thm)],[c_0_81,c_0_77]) ).
cnf(c_0_97,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(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_82]) ).
cnf(c_0_98,plain,
c_Fun_Oid(tc_HOL_Obool) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_99,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_100,plain,
! [X523,X524] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X524,tc_HOL_Obool)),X523),X523) = c_Orderings_Obot__class_Obot(tc_fun(X524,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
cnf(c_0_101,plain,
( hAPP(c_fconj,hAPP(c_fNot,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_102,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)),
inference(rw,[status(thm)],[c_0_88,c_0_77]) ).
fof(c_0_103,plain,
! [X109] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X109),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_104,plain,
( ~ hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk48_1(X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_105,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_91,c_0_74]) ).
fof(c_0_106,plain,
! [X1925,X1926,X1927,X1928] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1928),X1927))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1926),hAPP(c_Set_Oimage(X1928,X1926,X1925),X1927))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])])]) ).
fof(c_0_107,plain,
! [X5706,X5707] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X5707),X5706))
| hAPP(c_Finite__Set_Ocard(X5707),X5706) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])]) ).
cnf(c_0_108,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_109,plain,
hAPP(c_Int_Onat,c_Int_OBit0(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))))) = 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)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_96]) ).
cnf(c_0_110,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_97,c_0_65]) ).
cnf(c_0_111,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot)) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_98]) ).
cnf(c_0_112,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)),X3) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_65]),c_0_65]) ).
cnf(c_0_113,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_114,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
fof(c_0_115,plain,
! [X3972] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3972),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_103])]) ).
cnf(c_0_116,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_104,c_0_105]) ).
cnf(c_0_117,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_106]) ).
cnf(c_0_118,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_107]) ).
cnf(c_0_119,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)],[inference(rw,[status(thm)],[c_0_108,c_0_94]),c_0_95]),c_0_96]),c_0_109]),c_0_80]) ).
cnf(c_0_120,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_113]),c_0_114]) ).
cnf(c_0_121,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_122,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_116,c_0_117]) ).
cnf(c_0_123,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_118,c_0_80]) ).
cnf(c_0_124,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_121,c_0_80]) ).
cnf(c_0_126,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),hAPP(c_fconj,hAPP(c_fNot,hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))))),
inference(spm,[status(thm)],[c_0_122,c_0_120]) ).
cnf(c_0_127,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]),c_0_126]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SWW372+1 : TPTP v8.2.0. Released v5.2.0.
% 0.04/0.08 % Command : run_E %s %d THM
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Wed Jun 19 09:16:53 EDT 2024
% 0.09/0.28 % CPUTime :
% 1.39/1.56 Running first-order theorem proving
% 1.39/1.56 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.p5LxNViyJ1/E---3.1_23358.p
% 142.39/20.53 # Version: 3.2.0
% 142.39/20.53 # Preprocessing class: FMLMSLSMSSSNFFN.
% 142.39/20.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 142.39/20.53 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 142.39/20.53 # Starting new_bool_3 with 300s (1) cores
% 142.39/20.53 # Starting new_bool_1 with 300s (1) cores
% 142.39/20.53 # Starting sh5l with 300s (1) cores
% 142.39/20.53 # new_bool_3 with pid 23438 completed with status 0
% 142.39/20.53 # Result found by new_bool_3
% 142.39/20.53 # Preprocessing class: FMLMSLSMSSSNFFN.
% 142.39/20.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 142.39/20.53 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 142.39/20.53 # Starting new_bool_3 with 300s (1) cores
% 142.39/20.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 142.39/20.53 # Search class: FGHSM-SMLM33-DFFFFFNN
% 142.39/20.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 142.39/20.53 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 142.39/20.53 # SAT001_MinMin_p005000_rr with pid 23442 completed with status 0
% 142.39/20.53 # Result found by SAT001_MinMin_p005000_rr
% 142.39/20.53 # Preprocessing class: FMLMSLSMSSSNFFN.
% 142.39/20.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 142.39/20.53 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 142.39/20.53 # Starting new_bool_3 with 300s (1) cores
% 142.39/20.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 142.39/20.53 # Search class: FGHSM-SMLM33-DFFFFFNN
% 142.39/20.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 142.39/20.53 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 142.39/20.53 # Preprocessing time : 0.074 s
% 142.39/20.53 # Presaturation interreduction done
% 142.39/20.53
% 142.39/20.53 # Proof found!
% 142.39/20.53 # SZS status ContradictoryAxioms
% 142.39/20.53 # SZS output start CNFRefutation
% See solution above
% 142.39/20.53 # Parsed axioms : 5251
% 142.39/20.53 # Removed by relevancy pruning/SinE : 3168
% 142.39/20.53 # Initial clauses : 3038
% 142.39/20.53 # Removed in clause preprocessing : 90
% 142.39/20.53 # Initial clauses in saturation : 2948
% 142.39/20.53 # Processed clauses : 23568
% 142.39/20.53 # ...of these trivial : 780
% 142.39/20.53 # ...subsumed : 13104
% 142.39/20.53 # ...remaining for further processing : 9684
% 142.39/20.53 # Other redundant clauses eliminated : 2871
% 142.39/20.53 # Clauses deleted for lack of memory : 0
% 142.39/20.53 # Backward-subsumed : 182
% 142.39/20.53 # Backward-rewritten : 600
% 142.39/20.53 # Generated clauses : 526826
% 142.39/20.53 # ...of the previous two non-redundant : 509046
% 142.39/20.53 # ...aggressively subsumed : 0
% 142.39/20.53 # Contextual simplify-reflections : 22
% 142.39/20.53 # Paramodulations : 523892
% 142.39/20.53 # Factorizations : 12
% 142.39/20.53 # NegExts : 0
% 142.39/20.53 # Equation resolutions : 2955
% 142.39/20.53 # Disequality decompositions : 0
% 142.39/20.53 # Total rewrite steps : 76351
% 142.39/20.53 # ...of those cached : 60614
% 142.39/20.53 # Propositional unsat checks : 1
% 142.39/20.53 # Propositional check models : 0
% 142.39/20.53 # Propositional check unsatisfiable : 0
% 142.39/20.53 # Propositional clauses : 0
% 142.39/20.53 # Propositional clauses after purity: 0
% 142.39/20.53 # Propositional unsat core size : 0
% 142.39/20.53 # Propositional preprocessing time : 0.000
% 142.39/20.53 # Propositional encoding time : 0.177
% 142.39/20.53 # Propositional solver time : 0.077
% 142.39/20.53 # Success case prop preproc time : 0.000
% 142.39/20.53 # Success case prop encoding time : 0.000
% 142.39/20.53 # Success case prop solver time : 0.000
% 142.39/20.53 # Current number of processed clauses : 6496
% 142.39/20.53 # Positive orientable unit clauses : 861
% 142.39/20.53 # Positive unorientable unit clauses: 58
% 142.39/20.53 # Negative unit clauses : 972
% 142.39/20.53 # Non-unit-clauses : 4605
% 142.39/20.53 # Current number of unprocessed clauses: 465039
% 142.39/20.53 # ...number of literals in the above : 1333014
% 142.39/20.53 # Current number of archived formulas : 0
% 142.39/20.53 # Current number of archived clauses : 2957
% 142.39/20.53 # Clause-clause subsumption calls (NU) : 3620666
% 142.39/20.53 # Rec. Clause-clause subsumption calls : 1762852
% 142.39/20.53 # Non-unit clause-clause subsumptions : 6896
% 142.39/20.53 # Unit Clause-clause subsumption calls : 260538
% 142.39/20.53 # Rewrite failures with RHS unbound : 415
% 142.39/20.53 # BW rewrite match attempts : 16449
% 142.39/20.53 # BW rewrite match successes : 825
% 142.39/20.53 # Condensation attempts : 0
% 142.39/20.53 # Condensation successes : 0
% 142.39/20.53 # Termbank termtop insertions : 14671993
% 142.39/20.53 # Search garbage collected termcells : 68885
% 142.39/20.53
% 142.39/20.53 # -------------------------------------------------
% 142.39/20.53 # User time : 17.883 s
% 142.39/20.53 # System time : 0.466 s
% 142.39/20.53 # Total time : 18.349 s
% 142.39/20.53 # Maximum resident set size: 18480 pages
% 142.39/20.53
% 142.39/20.53 # -------------------------------------------------
% 142.39/20.53 # User time : 18.131 s
% 142.39/20.53 # System time : 0.478 s
% 142.39/20.53 # Total time : 18.609 s
% 142.39/20.53 # Maximum resident set size: 9564 pages
% 142.39/20.53 % E---3.1 exiting
% 142.39/20.53 % E exiting
%------------------------------------------------------------------------------