%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SCT161+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n004.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 : 600s
% DateTime : Mon Jul 18 21:23:30 EDT 2022
% Result : Theorem 0.35s 11.54s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 86 ( 35 unt; 0 def)
% Number of atoms : 183 ( 41 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 170 ( 73 ~; 63 |; 12 &)
% ( 7 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-4 aty)
% Number of variables : 192 ( 35 sgn 114 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X24] :
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X24,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
=> c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X24,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_finite__subset,axiom,
! [X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( c_Finite__Set_Ofinite(X5,X30)
=> c_Finite__Set_Ofinite(X5,X25) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_finite__subset) ).
fof(fact_subset__UNIV,axiom,
! [X25,X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_the__inv__into__onto,axiom,
! [X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> c_Set_Oimage(X7,X5,c_Fun_Othe__inv__into(X5,X7,X25,X2),c_Set_Oimage(X5,X7,X2,X25)) = X25 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_surjh,axiom,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_surjh) ).
fof(fact_finite__atLeastLessThan,axiom,
! [X48,X49] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X49,X48)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(fact_finite__option__UNIV,axiom,
! [X5] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X5),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X5),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_finite__surj,axiom,
! [X2,X30,X7,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X30),c_Set_Oimage(X5,X7,X2,X25)))
=> c_Finite__Set_Ofinite(X7,X30) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_finite__surj) ).
fof(fact_less__not__refl,axiom,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X8)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_less__not__refl) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X58] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X58)
<=> ? [X29] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X58))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X29)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_gr__implies__not0,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> X8 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_greaterThan__iff,axiom,
! [X52,X44,X5] :
( class_Orderings_Oord(X5)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord__class_OgreaterThan(X5,X52)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X52),X44)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_all__not__in__conv,axiom,
! [X25,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
<=> X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_rangeI,axiom,
! [X7,X4,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X4)),c_Set_Oimage(X7,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_rangeI) ).
fof(fact_mem__def,axiom,
! [X25,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
<=> hBOOL(hAPP(X25,X4)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_mem__def) ).
fof(fact_greaterThan__0,axiom,
c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_greaterThan__0) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(fact_ex__in__conv,axiom,
! [X25,X5] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
<=> X25 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_ex__in__conv) ).
fof(fact_gr0I,axiom,
! [X8] :
( X8 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_gr0I) ).
fof(fact_finite__imageD,axiom,
! [X25,X2,X7,X5] :
( c_Finite__Set_Ofinite(X5,c_Set_Oimage(X7,X5,X2,X25))
=> ( c_Fun_Oinj__on(X7,X5,X2,X25)
=> c_Finite__Set_Ofinite(X7,X25) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_finite__imageD) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_inj__on__def,axiom,
! [X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
=> ! [X32] :
( hBOOL(hAPP(hAPP(c_member(X5),X32),X25))
=> ( hAPP(X2,X3) = hAPP(X2,X32)
=> X3 = X32 ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_inj__on__def) ).
fof(c_0_22,plain,
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
& c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])]) ).
fof(c_0_23,plain,
! [X31,X32,X33] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33,tc_HOL_Obool),X32),X31))
| ~ c_Finite__Set_Ofinite(X33,X31)
| c_Finite__Set_Ofinite(X33,X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(c_0_24,plain,
! [X26,X27] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27,tc_HOL_Obool),X26),c_Orderings_Otop__class_Otop(tc_fun(X27,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(c_0_25,plain,
! [X26,X27,X28,X29] :
( ~ c_Fun_Oinj__on(X29,X28,X27,X26)
| c_Set_Oimage(X28,X29,c_Fun_Othe__inv__into(X29,X28,X26,X27),c_Set_Oimage(X29,X28,X27,X26)) = X26 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).
cnf(c_0_26,plain,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[fact_surjh]) ).
fof(c_0_28,plain,
! [X50,X51] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X51,X50)),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).
cnf(c_0_29,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(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_24]) ).
fof(c_0_31,plain,
! [X6,X6] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X6),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X6),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X6,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X6),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X6),tc_HOL_Obool))) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])])])]) ).
fof(c_0_32,plain,
! [X31,X32,X33,X34,X35] :
( ~ c_Finite__Set_Ofinite(X35,X34)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33,tc_HOL_Obool),X32),c_Set_Oimage(X35,X33,X31,X34)))
| c_Finite__Set_Ofinite(X33,X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
cnf(c_0_33,plain,
( c_Set_Oimage(X1,X2,c_Fun_Othe__inv__into(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X4,X3)) = X3
| ~ c_Fun_Oinj__on(X2,X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_36,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_37,plain,
! [X9] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X9)),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__not__refl])]) ).
fof(c_0_38,plain,
! [X59,X61,X59,X62] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X59)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X61),X59))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),esk37_1(X59))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk38_2(X59,X62)),X59))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X59) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk38_2(X59,X62)),X62))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X59) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded])])])])])])]) ).
cnf(c_0_39,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,plain,
( c_Finite__Set_Ofinite(tc_Option_Ooption(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
| ~ c_Finite__Set_Ofinite(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi,c_Fun_Othe__inv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),esk2_0),c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_43,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
fof(c_0_44,plain,
! [X13,X14] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X13))
| X13 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])])])]) ).
fof(c_0_45,plain,
! [X53,X54,X55] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X55),X54),c_SetInterval_Oord__class_OgreaterThan(X55,X53)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X55),X53),X54))
| ~ class_Orderings_Oord(X55) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X55),X53),X54))
| hBOOL(hAPP(hAPP(c_member(X55),X54),c_SetInterval_Oord__class_OgreaterThan(X55,X53)))
| ~ class_Orderings_Oord(X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).
fof(c_0_46,plain,
! [X26,X27,X26,X27,X29] :
( ( hBOOL(hAPP(hAPP(c_member(X27),esk47_2(X26,X27)),X26))
| X26 = c_Orderings_Obot__class_Obot(tc_fun(X27,tc_HOL_Obool)) )
& ( X26 != c_Orderings_Obot__class_Obot(tc_fun(X27,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X27),X29),X26)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__not__in__conv])])])])])])]) ).
fof(c_0_47,plain,
! [X8,X9,X10,X11] : hBOOL(hAPP(hAPP(c_member(X11),hAPP(X10,X9)),c_Set_Oimage(X8,X11,X10,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_48,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_49,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk37_1(X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_50,plain,
! [X26,X27,X28,X26,X27,X28] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X28),X27),X26))
| hBOOL(hAPP(X26,X27)) )
& ( ~ hBOOL(hAPP(X26,X27))
| hBOOL(hAPP(hAPP(c_member(X28),X27),X26)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])])]) ).
cnf(c_0_51,plain,
( c_Finite__Set_Ofinite(tc_Option_Ooption(X1),X2)
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_52,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_30])]) ).
cnf(c_0_53,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_SetInterval_Oord__class_OgreaterThan(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,plain,
c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_greaterThan__0]) ).
cnf(c_0_56,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
fof(c_0_57,plain,
! [X26,X27,X28,X26,X27] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X27),X28),X26))
| X26 != c_Orderings_Obot__class_Obot(tc_fun(X27,tc_HOL_Obool)) )
& ( X26 = c_Orderings_Obot__class_Obot(tc_fun(X27,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X27),esk48_2(X26,X27)),X26)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__in__conv])])])])])]) ).
cnf(c_0_58,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk37_1(X1)),X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_61,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_62,plain,
! [X9] :
( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(c_0_63,plain,
! [X26,X27,X28,X29] :
( ~ c_Finite__Set_Ofinite(X29,c_Set_Oimage(X28,X29,X27,X26))
| ~ c_Fun_Oinj__on(X28,X29,X27,X26)
| c_Finite__Set_Ofinite(X28,X26) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
cnf(c_0_64,plain,
c_Finite__Set_Ofinite(tc_Option_Ooption(tc_Arrow__Order__Mirabelle_Oindi),X1),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_65,plain,
! [X13] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X13,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_66,plain,
! [X33,X34,X35,X36,X37,X38,X33,X34,X35,X36] :
( ( ~ c_Fun_Oinj__on(X36,X35,X34,X33)
| ~ hBOOL(hAPP(hAPP(c_member(X36),X37),X33))
| ~ hBOOL(hAPP(hAPP(c_member(X36),X38),X33))
| hAPP(X34,X37) != hAPP(X34,X38)
| X37 = X38 )
& ( hBOOL(hAPP(hAPP(c_member(X36),esk9_4(X33,X34,X35,X36)),X33))
| c_Fun_Oinj__on(X36,X35,X34,X33) )
& ( hBOOL(hAPP(hAPP(c_member(X36),esk10_4(X33,X34,X35,X36)),X33))
| c_Fun_Oinj__on(X36,X35,X34,X33) )
& ( hAPP(X34,esk9_4(X33,X34,X35,X36)) = hAPP(X34,esk10_4(X33,X34,X35,X36))
| c_Fun_Oinj__on(X36,X35,X34,X33) )
& ( esk9_4(X33,X34,X35,X36) != esk10_4(X33,X34,X35,X36)
| c_Fun_Oinj__on(X36,X35,X34,X33) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__def])])])])])])]) ).
cnf(c_0_67,plain,
( esk37_1(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(spm,[status(thm)],[c_0_53,c_0_49]) ).
cnf(c_0_68,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_69,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk48_2(X2,X1)),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_70,plain,
c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,plain,
( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(X1,esk37_1(X1))) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,X3,X4,X2)
| ~ c_Finite__Set_Ofinite(X3,c_Set_Oimage(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_74,plain,
c_Finite__Set_Ofinite(tc_Option_Ooption(tc_Option_Ooption(tc_Arrow__Order__Mirabelle_Oindi)),X1),
inference(spm,[status(thm)],[c_0_51,c_0_64]) ).
cnf(c_0_75,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(X3,esk9_4(X4,X3,X2,X1)) = hAPP(X3,esk10_4(X4,X3,X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| esk9_4(X4,X3,X2,X1) != esk10_4(X4,X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_78,plain,
( esk37_1(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_67,c_0_61]) ).
cnf(c_0_79,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk48_2(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_80,plain,
( esk37_1(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_81,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,tc_Option_Ooption(tc_Option_Ooption(tc_Arrow__Order__Mirabelle_Oindi)),X3,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,plain,
c_Fun_Oinj__on(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_75]),c_0_77]) ).
cnf(c_0_83,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_84,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SCT161+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 08:38:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.35/11.54 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.35/11.54 # Preprocessing time : 0.080 s
% 0.35/11.54
% 0.35/11.54 # Proof found!
% 0.35/11.54 # SZS status Theorem
% 0.35/11.54 # SZS output start CNFRefutation
% See solution above
% 0.35/11.54 # Proof object total steps : 86
% 0.35/11.54 # Proof object clause steps : 45
% 0.35/11.54 # Proof object formula steps : 41
% 0.35/11.54 # Proof object conjectures : 0
% 0.35/11.54 # Proof object clause conjectures : 0
% 0.35/11.54 # Proof object formula conjectures : 0
% 0.35/11.54 # Proof object initial clauses used : 24
% 0.35/11.54 # Proof object initial formulas used : 22
% 0.35/11.54 # Proof object generating inferences : 19
% 0.35/11.54 # Proof object simplifying inferences : 14
% 0.35/11.54 # Training examples: 0 positive, 0 negative
% 0.35/11.54 # Parsed axioms : 535
% 0.35/11.54 # Removed by relevancy pruning/SinE : 0
% 0.35/11.54 # Initial clauses : 830
% 0.35/11.54 # Removed in clause preprocessing : 48
% 0.35/11.54 # Initial clauses in saturation : 782
% 0.35/11.54 # Processed clauses : 14216
% 0.35/11.54 # ...of these trivial : 395
% 0.35/11.54 # ...subsumed : 9808
% 0.35/11.54 # ...remaining for further processing : 4013
% 0.35/11.54 # Other redundant clauses eliminated : 488
% 0.35/11.54 # Clauses deleted for lack of memory : 194573
% 0.35/11.54 # Backward-subsumed : 225
% 0.35/11.54 # Backward-rewritten : 829
% 0.35/11.54 # Generated clauses : 297144
% 0.35/11.54 # ...of the previous two non-trivial : 287030
% 0.35/11.54 # Contextual simplify-reflections : 5846
% 0.35/11.54 # Paramodulations : 296497
% 0.35/11.54 # Factorizations : 18
% 0.35/11.54 # Equation resolutions : 635
% 0.35/11.54 # Current number of processed clauses : 2898
% 0.35/11.54 # Positive orientable unit clauses : 333
% 0.35/11.54 # Positive unorientable unit clauses: 38
% 0.35/11.54 # Negative unit clauses : 305
% 0.35/11.54 # Non-unit-clauses : 2222
% 0.35/11.54 # Current number of unprocessed clauses: 59052
% 0.35/11.54 # ...number of literals in the above : 191840
% 0.35/11.54 # Current number of archived formulas : 0
% 0.35/11.54 # Current number of archived clauses : 1054
% 0.35/11.54 # Clause-clause subsumption calls (NU) : 7360303
% 0.35/11.54 # Rec. Clause-clause subsumption calls : 2447060
% 0.35/11.54 # Non-unit clause-clause subsumptions : 11413
% 0.35/11.54 # Unit Clause-clause subsumption calls : 110908
% 0.35/11.54 # Rewrite failures with RHS unbound : 470
% 0.35/11.54 # BW rewrite match attempts : 12003
% 0.35/11.54 # BW rewrite match successes : 501
% 0.35/11.54 # Condensation attempts : 0
% 0.35/11.54 # Condensation successes : 0
% 0.35/11.54 # Termbank termtop insertions : 10750988
% 0.35/11.54
% 0.35/11.54 # -------------------------------------------------
% 0.35/11.54 # User time : 10.396 s
% 0.35/11.54 # System time : 0.134 s
% 0.35/11.54 # Total time : 10.530 s
% 0.35/11.54 # Maximum resident set size: 148816 pages
%------------------------------------------------------------------------------