TSTP Solution File: SWW332+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SWW332+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n009.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 20:11:03 EDT 2023
% Result : ContradictoryAxioms 15.54s 4.28s
% Output : CNFRefutation 15.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 71 ( 58 unt; 0 def)
% Number of atoms : 92 ( 50 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 14 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 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 : 107 ( 12 sgn; 59 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__mem__eq,axiom,
! [X20,X8] : hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X20)) = X20,
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X6,X8] : hAPP(c_Set_OCollect(X8),X6) = X6,
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_Collect__def) ).
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.fvVR7oHG31/E---3.1_29060.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.fvVR7oHG31/E---3.1_29060.p',fact_Pls__def) ).
fof(fact_less__irrefl__nat,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17)),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_less__irrefl__nat) ).
fof(help_c__COMBC__1,axiom,
! [X29,X4,X6,X8,X41,X22] : hAPP(hAPP(hAPP(c_COMBC(X22,X41,X8),X6),X4),X29) = hAPP(hAPP(X6,X29),X4),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',help_c__COMBC__1) ).
fof(fact_number__of__is__id,axiom,
! [X104] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X104) = X104,
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_number__of__is__id) ).
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/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_One__nat__def) ).
fof(fact_nat__number__of__def,axiom,
! [X151] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X151) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X151)),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_nat__number__of__def) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X7] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7)),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_less__eq__Suc__le__raw) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X123] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X123))
<=> ? [X143] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X123))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X143)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.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.fvVR7oHG31/E---3.1_29060.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/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_card__infinite,axiom,
! [X20,X8] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X20))
=> hAPP(c_Finite__Set_Ocard(X8),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_card__infinite) ).
fof(fact_rangeI,axiom,
! [X22,X23,X2,X8] : hBOOL(hAPP(hAPP(c_member(X8),hAPP(X2,X23)),hAPP(c_Set_Oimage(X22,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X22,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_rangeI) ).
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.fvVR7oHG31/E---3.1_29060.p',fact_semiring__norm_I115_J) ).
fof(fact_Zero__not__Suc,axiom,
! [X59] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X59),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_Zero__not__Suc) ).
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.fvVR7oHG31/E---3.1_29060.p',fact_card__UNIV__bool) ).
fof(fact_finite__imageI,axiom,
! [X105,X22,X126,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X126))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X22),hAPP(c_Set_Oimage(X8,X22,X105),X126))) ),
file('/export/starexec/sandbox2/tmp/tmp.fvVR7oHG31/E---3.1_29060.p',fact_finite__imageI) ).
fof(c_0_19,plain,
! [X4684,X4685] : hAPP(c_Set_OCollect(X4685),hAPP(hAPP(c_COMBC(X4685,tc_fun(X4685,tc_HOL_Obool),tc_HOL_Obool),c_member(X4685)),X4684)) = X4684,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_20,plain,
! [X4707,X4708] : hAPP(c_Set_OCollect(X4708),X4707) = X4707,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
cnf(c_0_21,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_22,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_23,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(c_0_24,plain,
! [X2432,X2433,X2434,X2435,X2436,X2437] : hAPP(hAPP(hAPP(c_COMBC(X2437,X2436,X2435),X2434),X2433),X2432) = hAPP(hAPP(X2434,X2432),X2433),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_25,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_26,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_27,plain,
! [X3067] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X3067) = X3067,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
cnf(c_0_28,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_29,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_30,plain,
! [X5375] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5375) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5375)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
fof(c_0_31,plain,
! [X1974] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1974),X1974)),
inference(variable_rename,[status(thm)],[c_0_23]) ).
fof(c_0_32,plain,
! [X1056] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1056) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1056)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_33,plain,
! [X2034,X2036,X2037,X2038] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2034))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2036),X2034))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2036),esk51_1(X2034))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk52_2(X2037,X2038)),X2037))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2037)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk52_2(X2037,X2038)),X2038))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2037)) ) ),
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_34,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,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_25,c_0_26]) ).
cnf(c_0_36,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_37,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,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_39,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_40,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_30]) ).
fof(c_0_41,plain,
! [X20,X8] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X20))
=> hAPP(c_Finite__Set_Ocard(X8),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
cnf(c_0_42,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,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_32]) ).
cnf(c_0_44,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk51_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_33]) ).
cnf(c_0_45,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_46,plain,
! [X597,X598,X599,X600] : hBOOL(hAPP(hAPP(c_member(X600),hAPP(X599,X598)),hAPP(c_Set_Oimage(X597,X600,X599),c_Orderings_Otop__class_Otop(tc_fun(X597,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_47,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_48,plain,
c_Int_OBit1(c_Int_OPls) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_49,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)],[c_0_38,c_0_39]) ).
cnf(c_0_50,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X1),
inference(rw,[status(thm)],[c_0_40,c_0_37]) ).
fof(c_0_51,plain,
! [X3991,X3992] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3992),X3991))
| hAPP(c_Finite__Set_Ocard(X3992),X3991) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
fof(c_0_52,plain,
! [X938] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X938),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_53,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_42,c_0_43]) ).
cnf(c_0_54,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk51_1(X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,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_46]) ).
cnf(c_0_56,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_57,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_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_47,c_0_48]),c_0_49]),c_0_50]),c_0_29]) ).
cnf(c_0_58,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_51]) ).
cnf(c_0_59,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
( ~ hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk51_1(X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,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_55,c_0_45]) ).
fof(c_0_62,plain,
! [X568,X569,X570,X571] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X571),X570))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X569),hAPP(c_Set_Oimage(X571,X569,X568),X570))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
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_56,c_0_48]),c_0_49]),c_0_50]),c_0_57]) ).
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_58,c_0_29]) ).
cnf(c_0_65,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_59,c_0_29]) ).
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_60,c_0_61]) ).
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_62]) ).
cnf(c_0_68,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_69,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_70,plain,
$false,
inference(sr,[status(thm)],[c_0_68,c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWW332+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.10 % Command : run_E %s %d THM
% 0.08/0.29 % Computer : n009.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 2400
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Oct 2 22:12:59 EDT 2023
% 0.08/0.30 % CPUTime :
% 1.29/1.49 Running first-order model finding
% 1.29/1.49 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.fvVR7oHG31/E---3.1_29060.p
% 15.54/4.28 # Version: 3.1pre001
% 15.54/4.28 # Preprocessing class: FMLMSMSMSSSNFFN.
% 15.54/4.28 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.54/4.28 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.54/4.28 # Starting new_bool_3 with 300s (1) cores
% 15.54/4.28 # Starting new_bool_1 with 300s (1) cores
% 15.54/4.28 # Starting sh5l with 300s (1) cores
% 15.54/4.28 # new_bool_1 with pid 29139 completed with status 0
% 15.54/4.28 # Result found by new_bool_1
% 15.54/4.28 # Preprocessing class: FMLMSMSMSSSNFFN.
% 15.54/4.28 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.54/4.28 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.54/4.28 # Starting new_bool_3 with 300s (1) cores
% 15.54/4.28 # Starting new_bool_1 with 300s (1) cores
% 15.54/4.28 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 15.54/4.28 # Search class: FGHSM-SMLM33-DFFFFFNN
% 15.54/4.28 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 15.54/4.28 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 15.54/4.28 # SAT001_MinMin_p005000_rr with pid 29142 completed with status 0
% 15.54/4.28 # Result found by SAT001_MinMin_p005000_rr
% 15.54/4.28 # Preprocessing class: FMLMSMSMSSSNFFN.
% 15.54/4.28 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.54/4.28 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 15.54/4.28 # Starting new_bool_3 with 300s (1) cores
% 15.54/4.28 # Starting new_bool_1 with 300s (1) cores
% 15.54/4.28 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 15.54/4.28 # Search class: FGHSM-SMLM33-DFFFFFNN
% 15.54/4.28 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 15.54/4.28 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 15.54/4.28 # Preprocessing time : 0.044 s
% 15.54/4.28 # Presaturation interreduction done
% 15.54/4.28
% 15.54/4.28 # Proof found!
% 15.54/4.28 # SZS status ContradictoryAxioms
% 15.54/4.28 # SZS output start CNFRefutation
% See solution above
% 15.54/4.28 # Parsed axioms : 5228
% 15.54/4.28 # Removed by relevancy pruning/SinE : 3761
% 15.54/4.28 # Initial clauses : 2235
% 15.54/4.28 # Removed in clause preprocessing : 70
% 15.54/4.28 # Initial clauses in saturation : 2165
% 15.54/4.28 # Processed clauses : 9591
% 15.54/4.28 # ...of these trivial : 346
% 15.54/4.28 # ...subsumed : 4997
% 15.54/4.28 # ...remaining for further processing : 4248
% 15.54/4.28 # Other redundant clauses eliminated : 1713
% 15.54/4.28 # Clauses deleted for lack of memory : 0
% 15.54/4.28 # Backward-subsumed : 98
% 15.54/4.28 # Backward-rewritten : 176
% 15.54/4.28 # Generated clauses : 95650
% 15.54/4.28 # ...of the previous two non-redundant : 89928
% 15.54/4.28 # ...aggressively subsumed : 0
% 15.54/4.28 # Contextual simplify-reflections : 8
% 15.54/4.28 # Paramodulations : 93914
% 15.54/4.28 # Factorizations : 12
% 15.54/4.28 # NegExts : 0
% 15.54/4.28 # Equation resolutions : 1747
% 15.54/4.28 # Total rewrite steps : 20844
% 15.54/4.28 # Propositional unsat checks : 0
% 15.54/4.28 # Propositional check models : 0
% 15.54/4.28 # Propositional check unsatisfiable : 0
% 15.54/4.28 # Propositional clauses : 0
% 15.54/4.28 # Propositional clauses after purity: 0
% 15.54/4.28 # Propositional unsat core size : 0
% 15.54/4.28 # Propositional preprocessing time : 0.000
% 15.54/4.28 # Propositional encoding time : 0.000
% 15.54/4.28 # Propositional solver time : 0.000
% 15.54/4.28 # Success case prop preproc time : 0.000
% 15.54/4.28 # Success case prop encoding time : 0.000
% 15.54/4.28 # Success case prop solver time : 0.000
% 15.54/4.28 # Current number of processed clauses : 2232
% 15.54/4.28 # Positive orientable unit clauses : 547
% 15.54/4.28 # Positive unorientable unit clauses: 44
% 15.54/4.28 # Negative unit clauses : 703
% 15.54/4.28 # Non-unit-clauses : 938
% 15.54/4.28 # Current number of unprocessed clauses: 73049
% 15.54/4.28 # ...number of literals in the above : 157049
% 15.54/4.28 # Current number of archived formulas : 0
% 15.54/4.28 # Current number of archived clauses : 1848
% 15.54/4.28 # Clause-clause subsumption calls (NU) : 311414
% 15.54/4.28 # Rec. Clause-clause subsumption calls : 182760
% 15.54/4.28 # Non-unit clause-clause subsumptions : 1132
% 15.54/4.28 # Unit Clause-clause subsumption calls : 28949
% 15.54/4.28 # Rewrite failures with RHS unbound : 317
% 15.54/4.28 # BW rewrite match attempts : 9361
% 15.54/4.28 # BW rewrite match successes : 651
% 15.54/4.28 # Condensation attempts : 0
% 15.54/4.28 # Condensation successes : 0
% 15.54/4.28 # Termbank termtop insertions : 2430553
% 15.54/4.28
% 15.54/4.28 # -------------------------------------------------
% 15.54/4.28 # User time : 2.367 s
% 15.54/4.28 # System time : 0.084 s
% 15.54/4.28 # Total time : 2.452 s
% 15.54/4.28 # Maximum resident set size: 15852 pages
% 15.54/4.28
% 15.54/4.28 # -------------------------------------------------
% 15.54/4.28 # User time : 2.621 s
% 15.54/4.28 # System time : 0.093 s
% 15.54/4.28 # Total time : 2.714 s
% 15.54/4.28 # Maximum resident set size: 9540 pages
% 15.54/4.28 % E---3.1 exiting
%------------------------------------------------------------------------------