TSTP Solution File: SWV823-1 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SWV823-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.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 20:07:56 EDT 2023
% Result : Unsatisfiable 190.15s 25.18s
% Output : CNFRefutation 190.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 36
% Syntax : Number of clauses : 121 ( 77 unt; 12 nHn; 40 RR)
% Number of literals : 177 ( 86 equ; 56 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 5 con; 0-4 aty)
% Number of variables : 257 ( 84 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Collect__neg__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_Collect__neg__eq_0) ).
cnf(cls_Collect__def_0,axiom,
hAPP(c_Collect(X1),X2) = X2,
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_Collect__def_0) ).
cnf(cls_Collect__imp__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2))),hAPP(c_Collect(X1),X3)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_Collect__imp__eq_0) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_COMBS__def_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_COMBB__def_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_COMBK__def_0) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_sup1CI_0) ).
cnf(cls_nat__rec__Suc_0,axiom,
c_Nat_Onat_Onat__rec(X1,X2,hAPP(c_Suc,X3),X4) = hAPP(hAPP(X2,X3),c_Nat_Onat_Onat__rec(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_nat__rec__Suc_0) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_double__complement_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_order__eq__iff_2) ).
cnf(cls_le__bool__def__raw_0,axiom,
c_lessequals(tc_bool) = c_implies,
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_le__bool__def__raw_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_diff__add__inverse2_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X2) = X1,
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_diff__add__inverse2_0) ).
cnf(cls_id__apply_0,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_id__apply_0) ).
cnf(cls_Collect__mem__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_Collect__mem__eq_0) ).
cnf(cls_exE__some_0,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_exE__some_0) ).
cnf(cls_le0_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_le0_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_COMBC__def_0) ).
cnf(cls_mono__Suc_0,axiom,
hBOOL(c_Orderings_Oorder__class_Omono(c_Suc,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_mono__Suc_0) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_ComplI_0) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_natgb_Oadd__r0__iff_0) ).
cnf(cls_add__Suc__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_add__Suc__right_0) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X1),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_Zero__neq__Suc_0) ).
cnf(cls_nat__minus__add__max_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_nat__minus__add__max_0) ).
cnf(cls_nat__add__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_nat__add__commute_0) ).
cnf(cls_sup__max_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1) = c_Orderings_Oord__class_Omax(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_sup__max_0) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',clsarity_nat__Orderings_Olinorder) ).
cnf(cls_add__Suc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_add__Suc_0) ).
cnf(cls_add__diff__inverse_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_add__diff__inverse_0) ).
cnf(cls_n__not__Suc__n_0,axiom,
X1 != hAPP(c_Suc,X1),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_n__not__Suc__n_0) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_linorder__not__less_1) ).
cnf(cls_less__Suc__eq__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_less__Suc__eq__le_0) ).
cnf(cls_mod__less__divisor_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_mod__less__divisor_0) ).
cnf(cls_zero__less__Suc_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Suc,X1))),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_zero__less__Suc_0) ).
cnf(cls_Suc__pred_0,axiom,
( hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))) = X1
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.SPUTzBw8ci/E---3.1_8102.p',cls_Suc__pred_0) ).
cnf(c_0_36,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_37,axiom,
hAPP(c_Collect(X1),X2) = X2,
cls_Collect__def_0 ).
cnf(c_0_38,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2))),hAPP(c_Collect(X1),X3)),
cls_Collect__imp__eq_0 ).
cnf(c_0_39,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_40,axiom,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
cls_COMBS__def_0 ).
cnf(c_0_41,plain,
hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_37]),c_0_39]),c_0_37]),c_0_37]) ).
cnf(c_0_42,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_43,axiom,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
cls_COMBK__def_0 ).
cnf(c_0_44,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
cls_sup1CI_0 ).
cnf(c_0_45,plain,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)),X3),X4) = hAPP(hAPP(c_implies,hAPP(X2,X4)),hAPP(X3,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_46,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),c_COMBK(X4,X5)),X6),X7) = X7,
inference(spm,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_47,axiom,
c_Nat_Onat_Onat__rec(X1,X2,hAPP(c_Suc,X3),X4) = hAPP(hAPP(X2,X3),c_Nat_Onat_Onat__rec(X1,X2,X3,X4)),
cls_nat__rec__Suc_0 ).
cnf(c_0_48,plain,
( hBOOL(hAPP(hAPP(c_implies,hAPP(X1,X2)),hAPP(X3,X2)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
hAPP(c_Nat_Onat_Onat__rec(X1,c_COMBS(X2,X3,X4),hAPP(c_Suc,c_COMBK(X5,X6)),X7),X8) = X8,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_51,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__eq__iff_2 ).
cnf(c_0_52,axiom,
c_lessequals(tc_bool) = c_implies,
cls_le__bool__def__raw_0 ).
cnf(c_0_53,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_54,plain,
( hBOOL(hAPP(hAPP(c_implies,hAPP(X1,X2)),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X2) = X1,
cls_diff__add__inverse2_0 ).
cnf(c_0_56,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_39]),c_0_39]) ).
cnf(c_0_57,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_implies,X2),X1))
| ~ hBOOL(hAPP(hAPP(c_implies,X1),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_58,plain,
( hBOOL(hAPP(hAPP(c_implies,X1),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_56]),c_0_42]) ).
cnf(c_0_60,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
cls_id__apply_0 ).
cnf(c_0_61,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_62,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_implies,X1),X2))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
cls_exE__some_0 ).
cnf(c_0_64,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1)),
cls_le0_0 ).
cnf(c_0_66,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_67,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_61,c_0_37]) ).
cnf(c_0_68,plain,
( X1 = X2
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_58]) ).
cnf(c_0_69,axiom,
hBOOL(c_Orderings_Oorder__class_Omono(c_Suc,tc_nat,tc_nat)),
cls_mono__Suc_0 ).
cnf(c_0_70,plain,
( hBOOL(hAPP(c_Not,c_Hilbert__Choice_OEps(c_Not,X1)))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
hBOOL(c_Nat_Onat_Onat__rec(X1,c_lessequals(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X2)),
inference(spm,[status(thm)],[c_0_65,c_0_47]) ).
cnf(c_0_72,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_ComplI_0 ).
cnf(c_0_73,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,plain,
( c_Orderings_Oorder__class_Omono(c_Suc,tc_nat,tc_nat) = X1
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,plain,
hBOOL(hAPP(c_Not,c_Hilbert__Choice_OEps(c_Not,X1))),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_39]),c_0_73]),c_0_42]),c_0_73]) ).
cnf(c_0_77,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_natgb_Oadd__r0__iff_0 ).
cnf(c_0_78,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc__right_0 ).
cnf(c_0_79,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X1),
cls_Zero__neq__Suc_0 ).
cnf(c_0_80,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X2),
cls_nat__minus__add__max_0 ).
cnf(c_0_81,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
cls_nat__add__commute_0 ).
cnf(c_0_82,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1) = c_Orderings_Oord__class_Omax(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__max_0 ).
cnf(c_0_83,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
clsarity_nat__Lattices_Oupper__semilattice ).
cnf(c_0_84,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder ).
cnf(c_0_85,plain,
hAPP(c_Not,c_Hilbert__Choice_OEps(c_Not,X1)) = c_Orderings_Oorder__class_Omono(c_Suc,tc_nat,tc_nat),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_86,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_49]) ).
cnf(c_0_87,plain,
hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_88,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc_0 ).
cnf(c_0_89,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X2),X1),
inference(rw,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,plain,
c_Orderings_Oord__class_Omax(tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]) ).
cnf(c_0_91,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
cls_add__diff__inverse_0 ).
cnf(c_0_92,plain,
hAPP(c_Not,c_Orderings_Oorder__class_Omono(c_Suc,tc_nat,tc_nat)) = c_Hilbert__Choice_OEps(c_Not,X1),
inference(spm,[status(thm)],[c_0_64,c_0_85]) ).
cnf(c_0_93,plain,
( c_Orderings_Oorder__class_Omono(c_Suc,tc_nat,tc_nat) = hAPP(c_Not,X1)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_86]) ).
cnf(c_0_94,plain,
hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))) != hAPP(c_Suc,X1),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X2),X1),
inference(rw,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(rw,[status(thm)],[c_0_91,c_0_89]) ).
cnf(c_0_97,axiom,
X1 != hAPP(c_Suc,X1),
cls_n__not__Suc__n_0 ).
cnf(c_0_98,plain,
( X1 = c_Hilbert__Choice_OEps(c_Not,X2)
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_64]) ).
cnf(c_0_99,plain,
hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2))) != hAPP(c_Suc,X2),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(rw,[status(thm)],[c_0_96,c_0_90]) ).
cnf(c_0_101,plain,
hBOOL(hAPP(c_Suc,c_Hilbert__Choice_OEps(c_Not,X1))),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_102,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_linorder__not__less_1 ).
cnf(c_0_103,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hAPP(c_Suc,hAPP(c_Suc,X1)) != hAPP(c_Suc,X2) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_104,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),hAPP(c_Suc,X2))) ),
cls_less__Suc__eq__le_0 ).
cnf(c_0_105,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
cls_mod__less__divisor_0 ).
cnf(c_0_106,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Suc,X1))),
cls_zero__less__Suc_0 ).
cnf(c_0_107,plain,
hBOOL(hAPP(c_Suc,c_Hilbert__Choice_OEps(c_Suc,X1))),
inference(spm,[status(thm)],[c_0_63,c_0_101]) ).
cnf(c_0_108,plain,
( X1 = X2
| hBOOL(X2)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_98]) ).
cnf(c_0_109,plain,
( hAPP(c_Suc,hAPP(c_Suc,X1)) != hAPP(c_Suc,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_84])]) ).
cnf(c_0_110,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Divides_Odiv__class_Omod(X1,hAPP(c_Suc,X2),tc_nat)),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106])]) ).
cnf(c_0_111,plain,
( hAPP(c_Suc,c_Hilbert__Choice_OEps(c_Suc,X1)) = X2
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_107]) ).
cnf(c_0_112,plain,
( hBOOL(hAPP(c_Suc,X1))
| hBOOL(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_108])]) ).
cnf(c_0_113,plain,
hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,hAPP(c_Suc,X2),tc_nat)) != hAPP(c_Suc,hAPP(c_Suc,X2)),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,axiom,
( hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))) = X1
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1)) ),
cls_Suc__pred_0 ).
cnf(c_0_115,plain,
hBOOL(hAPP(c_Suc,X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_79]) ).
cnf(c_0_116,plain,
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != hAPP(c_Suc,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_117,plain,
( hAPP(c_Suc,X1) = X2
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_115]) ).
cnf(c_0_118,plain,
( hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))) != hAPP(c_Suc,X1)
| hAPP(c_Suc,c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) != hAPP(c_Suc,X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_103]) ).
cnf(c_0_119,plain,
hAPP(c_Suc,X1) = hAPP(c_Suc,X2),
inference(spm,[status(thm)],[c_0_117,c_0_115]) ).
cnf(c_0_120,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_118,c_0_119]),c_0_119]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV823-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n029.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 2400
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Oct 3 03:47:52 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.43/0.62 Running first-order model finding
% 0.43/0.62 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.SPUTzBw8ci/E---3.1_8102.p
% 190.15/25.18 # Version: 3.1pre001
% 190.15/25.18 # Preprocessing class: FSLMSMSMSSSNFFN.
% 190.15/25.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 190.15/25.18 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 190.15/25.18 # Starting new_bool_3 with 600s (2) cores
% 190.15/25.18 # Starting new_bool_1 with 300s (1) cores
% 190.15/25.18 # Starting sh5l with 300s (1) cores
% 190.15/25.18 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 8179 completed with status 0
% 190.15/25.18 # Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 190.15/25.18 # Preprocessing class: FSLMSMSMSSSNFFN.
% 190.15/25.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 190.15/25.18 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 190.15/25.18 # No SInE strategy applied
% 190.15/25.18 # Search class: FGHSM-FSLM32-DFFFFFNN
% 190.15/25.18 # Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 190.15/25.18 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 90s (1) cores
% 190.15/25.18 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 190.15/25.18 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 190.15/25.18 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 190.15/25.18 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 8189 completed with status 0
% 190.15/25.18 # Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 190.15/25.18 # Preprocessing class: FSLMSMSMSSSNFFN.
% 190.15/25.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 190.15/25.18 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 190.15/25.18 # No SInE strategy applied
% 190.15/25.18 # Search class: FGHSM-FSLM32-DFFFFFNN
% 190.15/25.18 # Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 190.15/25.18 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 90s (1) cores
% 190.15/25.18 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 190.15/25.18 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 190.15/25.18 # Preprocessing time : 0.014 s
% 190.15/25.18 # Presaturation interreduction done
% 190.15/25.18
% 190.15/25.18 # Proof found!
% 190.15/25.18 # SZS status Unsatisfiable
% 190.15/25.18 # SZS output start CNFRefutation
% See solution above
% 190.15/25.18 # Parsed axioms : 997
% 190.15/25.18 # Removed by relevancy pruning/SinE : 0
% 190.15/25.18 # Initial clauses : 997
% 190.15/25.18 # Removed in clause preprocessing : 0
% 190.15/25.18 # Initial clauses in saturation : 997
% 190.15/25.18 # Processed clauses : 25846
% 190.15/25.18 # ...of these trivial : 3485
% 190.15/25.18 # ...subsumed : 17766
% 190.15/25.18 # ...remaining for further processing : 4595
% 190.15/25.18 # Other redundant clauses eliminated : 3185
% 190.15/25.18 # Clauses deleted for lack of memory : 0
% 190.15/25.18 # Backward-subsumed : 101
% 190.15/25.18 # Backward-rewritten : 151
% 190.15/25.18 # Generated clauses : 1124679
% 190.15/25.18 # ...of the previous two non-redundant : 1010868
% 190.15/25.18 # ...aggressively subsumed : 0
% 190.15/25.18 # Contextual simplify-reflections : 2
% 190.15/25.18 # Paramodulations : 1121225
% 190.15/25.18 # Factorizations : 12
% 190.15/25.18 # NegExts : 0
% 190.15/25.18 # Equation resolutions : 3213
% 190.15/25.18 # Total rewrite steps : 290696
% 190.15/25.18 # Propositional unsat checks : 0
% 190.15/25.18 # Propositional check models : 0
% 190.15/25.18 # Propositional check unsatisfiable : 0
% 190.15/25.18 # Propositional clauses : 0
% 190.15/25.18 # Propositional clauses after purity: 0
% 190.15/25.18 # Propositional unsat core size : 0
% 190.15/25.18 # Propositional preprocessing time : 0.000
% 190.15/25.18 # Propositional encoding time : 0.000
% 190.15/25.18 # Propositional solver time : 0.000
% 190.15/25.18 # Success case prop preproc time : 0.000
% 190.15/25.18 # Success case prop encoding time : 0.000
% 190.15/25.18 # Success case prop solver time : 0.000
% 190.15/25.18 # Current number of processed clauses : 3302
% 190.15/25.18 # Positive orientable unit clauses : 1704
% 190.15/25.18 # Positive unorientable unit clauses: 208
% 190.15/25.18 # Negative unit clauses : 224
% 190.15/25.18 # Non-unit-clauses : 1166
% 190.15/25.18 # Current number of unprocessed clauses: 966549
% 190.15/25.18 # ...number of literals in the above : 1661895
% 190.15/25.18 # Current number of archived formulas : 0
% 190.15/25.18 # Current number of archived clauses : 1293
% 190.15/25.18 # Clause-clause subsumption calls (NU) : 506573
% 190.15/25.18 # Rec. Clause-clause subsumption calls : 293721
% 190.15/25.18 # Non-unit clause-clause subsumptions : 6828
% 190.15/25.18 # Unit Clause-clause subsumption calls : 40579
% 190.15/25.18 # Rewrite failures with RHS unbound : 6217
% 190.15/25.18 # BW rewrite match attempts : 260238
% 190.15/25.18 # BW rewrite match successes : 2431
% 190.15/25.18 # Condensation attempts : 0
% 190.15/25.18 # Condensation successes : 0
% 190.15/25.18 # Termbank termtop insertions : 33631100
% 190.15/25.18
% 190.15/25.18 # -------------------------------------------------
% 190.15/25.18 # User time : 23.099 s
% 190.15/25.18 # System time : 0.769 s
% 190.15/25.18 # Total time : 23.869 s
% 190.15/25.18 # Maximum resident set size: 3916 pages
% 190.15/25.18
% 190.15/25.18 # -------------------------------------------------
% 190.15/25.18 # User time : 91.850 s
% 190.15/25.18 # System time : 2.720 s
% 190.15/25.18 # Total time : 94.570 s
% 190.15/25.18 # Maximum resident set size: 2600 pages
% 190.15/25.18 % E---3.1 exiting
%------------------------------------------------------------------------------