%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW303+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:15 PM UTC 2026
% Result : ContradictoryAxioms 192.18s 34.25s
% Output : CNFRefutation 192.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 27
% Syntax : Number of formulae : 174 ( 107 unt; 0 def)
% Number of atoms : 267 ( 141 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 187 ( 94 ~; 75 |; 5 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 8 con; 0-3 aty)
% Number of variables : 320 ( 70 sgn 153 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__neg__eq,axiom,
! [X29,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X29)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_Collect__def,axiom,
! [X29,X5] : hAPP(c_Set_OCollect(X5),X29) = X29,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__mem__eq,axiom,
! [X16,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X16)) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_Compl__empty__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(help_c__COMBC__1,axiom,
! [X35,X30,X29,X5,X24,X17] : hAPP(hAPP(hAPP(c_COMBC(X17,X24,X5),X29),X30),X35) = hAPP(hAPP(X29,X35),X30),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBB__1,axiom,
! [X35,X30,X29,X24,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X24),X29),X30),X35) = hAPP(X29,hAPP(X30,X35)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_insert__absorb,axiom,
! [X16,X6,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X6),X16))
=> hAPP(hAPP(c_Set_Oinsert(X5),X6),X16) = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_top1I,axiom,
! [X18,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_Collect__empty__eq,axiom,
! [X29,X5] :
( hAPP(c_Set_OCollect(X5),X29) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X29,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__not__insert,axiom,
! [X16,X6,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X5),X6),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__not__insert) ).
fof(help_c__fNot__1,axiom,
! [X29] :
( ~ hBOOL(X29)
| ~ hBOOL(hAPP(c_fNot,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_ComplE,axiom,
! [X16,X21,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X16)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplE) ).
fof(fact_mem__def,axiom,
! [X16,X18,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X18),X16))
<=> hBOOL(hAPP(X16,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(help_c__COMBK__1,axiom,
! [X309,X308,X5,X59] : hAPP(hAPP(c_COMBK(X59,X5),X308),X309) = X308,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(conj_0,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_Procs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_double__complement,axiom,
! [X16,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)),X16)) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_number__of__is__id,axiom,
! [X126] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X126) = X126,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(fact_distinct_Osimps_I1_J,axiom,
! [X59] : hBOOL(hAPP(c_List_Odistinct(X59),c_List_Olist_ONil(X59))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact_disjoint__iff__not__equal,axiom,
! [X20,X16,X5] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X16),X20) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X16))
=> ! [X66] :
( hBOOL(hAPP(hAPP(c_member(X5),X66),X20))
=> X3 != X66 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(fact_the_Osimps,axiom,
! [X58,X59] : hAPP(c_Option_Othe(X59),hAPP(c_Option_Ooption_OSome(X59),X58)) = X58,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the_Osimps) ).
fof(fact_not__Cons__self,axiom,
! [X58,X59,X252] : X252 != hAPP(hAPP(c_List_Olist_OCons(X59),X58),X252),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(fact_Int__absorb,axiom,
! [X16,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X16),X16) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(fact_n__not__Suc__n,axiom,
! [X123] : X123 != hAPP(c_Nat_OSuc,X123),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_Zero__neq__Suc,axiom,
! [X124] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X124),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_add__eq__self__zero,axiom,
! [X123,X124] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X124),X123) = X124
=> X123 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_add__Suc__right,axiom,
! [X123,X124] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X124),hAPP(c_Nat_OSuc,X123)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X124),X123)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X124] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X124),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X124,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(c_0_27,plain,
! [X3786,X3787] : hAPP(c_Set_OCollect(X3787),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3787),c_fNot),X3786)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3787,tc_HOL_Obool)),hAPP(c_Set_OCollect(X3787),X3786)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_28,plain,
! [X3812,X3813] : hAPP(c_Set_OCollect(X3813),X3812) = X3812,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_29,plain,
! [X3835,X3836] : hAPP(c_Set_OCollect(X3836),hAPP(hAPP(c_COMBC(X3836,tc_fun(X3836,tc_HOL_Obool),tc_HOL_Obool),c_member(X3836)),X3835)) = X3835,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_30,plain,
! [X1539] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1539,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1539,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1539,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_31,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_27]) ).
cnf(c_0_32,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X2113,X2114,X2115,X2116,X2117,X2118] : hAPP(hAPP(hAPP(c_COMBC(X2118,X2117,X2116),X2115),X2114),X2113) = hAPP(hAPP(X2115,X2113),X2114),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_34,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_29]) ).
fof(c_0_35,plain,
! [X627,X628,X629,X630,X631,X632] : hAPP(hAPP(hAPP(c_COMBB(X632,X631,X630),X629),X628),X627) = hAPP(X629,hAPP(X628,X627)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_36,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,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_31,c_0_32]),c_0_32]) ).
fof(c_0_38,plain,
! [X793,X794,X795] :
( hAPP(hAPP(c_Set_Oinsert(X795),X794),X793) = X793
| ~ hBOOL(hAPP(hAPP(c_member(X795),X794),X793)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])])]) ).
cnf(c_0_39,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,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_34,c_0_32]) ).
fof(c_0_41,plain,
! [X1528,X1529] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1529,tc_HOL_Obool)),X1528)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_42,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_44,plain,
! [X29,X5] :
( hAPP(c_Set_OCollect(X5),X29) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X29,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_45,plain,
! [X16,X6,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X5),X6),X16),
inference(fof_simplification,[status(thm)],[fact_empty__not__insert]) ).
cnf(c_0_46,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(c_fNot,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_50,plain,
! [X29] :
( ~ hBOOL(X29)
| ~ hBOOL(hAPP(c_fNot,X29)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_51,plain,
! [X3814,X3815,X3816,X3817,X3819] :
( ( hAPP(c_Set_OCollect(X3819),X3817) = c_Orderings_Obot__class_Obot(tc_fun(X3819,tc_HOL_Obool))
| hBOOL(hAPP(X3817,esk79_1(X3817))) )
& ( ~ hBOOL(hAPP(X3814,X3816))
| hAPP(c_Set_OCollect(X3815),X3814) != c_Orderings_Obot__class_Obot(tc_fun(X3815,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_44])])])])])]) ).
fof(c_0_52,plain,
! [X693,X694,X695] : c_Orderings_Obot__class_Obot(tc_fun(X695,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X695),X694),X693),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_45])]) ).
cnf(c_0_53,plain,
( ~ hBOOL(hAPP(X3,X2))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3 ),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
hBOOL(hAPP(c_fNot,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_55,plain,
! [X16,X21,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X16)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X21),X16)) ),
inference(fof_simplification,[status(thm)],[fact_ComplE]) ).
fof(c_0_56,plain,
! [X329,X330,X331] :
( ( hBOOL(hAPP(hAPP(c_member(X331),X330),X329))
| ~ hBOOL(hAPP(X329,X330)) )
& ( hBOOL(hAPP(X329,X330))
| ~ hBOOL(hAPP(hAPP(c_member(X331),X330),X329)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])]) ).
fof(c_0_57,plain,
! [X3807] :
( ~ hBOOL(X3807)
| ~ hBOOL(hAPP(c_fNot,X3807)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_50])]) ).
cnf(c_0_58,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk79_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
hAPP(hAPP(c_Set_Oinsert(X1),hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X3)),c_fNot) = c_fNot,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_61,plain,
! [X3748,X3749,X3750,X3751] : hAPP(hAPP(c_COMBK(X3751,X3750),X3749),X3748) = X3749,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(c_0_62,plain,
! [X1808,X1809,X1810] :
( ~ hBOOL(hAPP(hAPP(c_member(X1810),X1809),X1808))
| ~ hBOOL(hAPP(hAPP(c_member(X1810),X1809),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1810,tc_HOL_Obool)),X1808))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
cnf(c_0_63,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_Procs)),
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_65,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
( hBOOL(hAPP(X1,esk79_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_58,c_0_32]) ).
cnf(c_0_67,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_fNot,
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_71,hypothesis,
hBOOL(hAPP(v_Procs,v_pn)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
~ hBOOL(esk79_1(c_fNot)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_73,plain,
( hBOOL(X3)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_66]),c_0_68]) ).
cnf(c_0_74,plain,
( ~ hBOOL(hAPP(X2,X3))
| hAPP(c_Set_OCollect(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_75,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X3))) ),
inference(rw,[status(thm)],[c_0_69,c_0_37]) ).
cnf(c_0_76,hypothesis,
hBOOL(hAPP(hAPP(c_member(X1),v_pn),v_Procs)),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = esk79_1(c_fNot),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_32])]) ).
fof(c_0_79,plain,
! [X1806,X1807] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1807,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1807,tc_HOL_Obool)),X1806)) = X1806,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_80,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(X1),v_pn),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),v_Procs))),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,plain,
( hBOOL(X1)
| esk79_1(c_fNot) = X1 ),
inference(spm,[status(thm)],[c_0_73,c_0_77]) ).
fof(c_0_82,plain,
! [X4333] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4333) = X4333,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
cnf(c_0_83,plain,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,esk79_1(X1))) ),
inference(spm,[status(thm)],[c_0_78,c_0_66]) ).
fof(c_0_84,plain,
! [X4077] : hBOOL(hAPP(c_List_Odistinct(X4077),c_List_Olist_ONil(X4077))),
inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).
cnf(c_0_85,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_79]) ).
cnf(c_0_86,hypothesis,
~ hBOOL(hAPP(c_fNot,hAPP(v_Procs,v_pn))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_47]),c_0_42]) ).
cnf(c_0_87,plain,
( hBOOL(X2)
| hBOOL(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_81,c_0_81]) ).
cnf(c_0_88,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_89,plain,
( ~ hBOOL(X2)
| hBOOL(esk79_1(c_Set_OCollect(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_32]),c_0_32]) ).
cnf(c_0_90,plain,
hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_91,plain,
! [X20,X16,X5] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X16),X20) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X16))
=> ! [X66] :
( hBOOL(hAPP(hAPP(c_member(X5),X66),X20))
=> X3 != X66 ) ) ),
inference(fof_simplification,[status(thm)],[fact_disjoint__iff__not__equal]) ).
cnf(c_0_92,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_85,c_0_37]),c_0_37]) ).
fof(c_0_93,plain,
! [X1122,X1123] : hAPP(c_Option_Othe(X1123),hAPP(c_Option_Ooption_OSome(X1123),X1122)) = X1122,
inference(variable_rename,[status(thm)],[fact_the_Osimps]) ).
cnf(c_0_94,hypothesis,
( hBOOL(X1)
| X1 = hAPP(c_fNot,hAPP(v_Procs,v_pn)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_95,plain,
( ~ hBOOL(X1)
| hBOOL(esk79_1(c_Int_Onumber__class_Onumber__of(tc_Int_Oint))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_88]),c_0_88]) ).
cnf(c_0_96,plain,
hBOOL(esk79_1(c_Set_OCollect(X1))),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
fof(c_0_97,plain,
! [X1917,X1918,X1919,X1920,X1921,X1922,X1923,X1924] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1924,tc_HOL_Obool)),X1923),X1922) = c_Orderings_Obot__class_Obot(tc_fun(X1924,tc_HOL_Obool))
| esk40_3(X1922,X1923,X1924) = esk41_3(X1922,X1923,X1924) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1924,tc_HOL_Obool)),X1923),X1922) = c_Orderings_Obot__class_Obot(tc_fun(X1924,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1924),esk41_3(X1922,X1923,X1924)),X1922)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1924,tc_HOL_Obool)),X1923),X1922) = c_Orderings_Obot__class_Obot(tc_fun(X1924,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1924),esk40_3(X1922,X1923,X1924)),X1923)) )
& ( X1920 != X1921
| ~ hBOOL(hAPP(hAPP(c_member(X1919),X1921),X1917))
| ~ hBOOL(hAPP(hAPP(c_member(X1919),X1920),X1918))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1919,tc_HOL_Obool)),X1918),X1917) != c_Orderings_Obot__class_Obot(tc_fun(X1919,tc_HOL_Obool)) ) ),
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)],[c_0_91])])])])])])]) ).
cnf(c_0_98,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_92]),c_0_42]) ).
cnf(c_0_99,plain,
hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_100,hypothesis,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = hAPP(c_fNot,hAPP(v_Procs,v_pn)) ),
inference(spm,[status(thm)],[c_0_65,c_0_94]) ).
cnf(c_0_101,plain,
hBOOL(esk79_1(c_Int_Onumber__class_Onumber__of(tc_Int_Oint))),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,plain,
( X4 != X5
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_103,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,hypothesis,
hAPP(c_fNot,esk79_1(c_Int_Onumber__class_Onumber__of(tc_Int_Oint))) = hAPP(c_fNot,hAPP(v_Procs,v_pn)),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
fof(c_0_105,plain,
! [X58,X59,X252] : X252 != hAPP(hAPP(c_List_Olist_OCons(X59),X58),X252),
inference(fof_simplification,[status(thm)],[fact_not__Cons__self]) ).
cnf(c_0_106,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(er,[status(thm)],[c_0_102]) ).
cnf(c_0_107,plain,
( esk79_1(c_fNot) != c_fNot
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_67,c_0_81]) ).
cnf(c_0_108,hypothesis,
esk79_1(c_Int_Onumber__class_Onumber__of(tc_Int_Oint)) = hAPP(v_Procs,v_pn),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_103]) ).
fof(c_0_109,plain,
! [X4389,X4390,X4391] : X4391 != hAPP(hAPP(c_List_Olist_OCons(X4390),X4389),X4391),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_105])]) ).
cnf(c_0_110,plain,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X3,X4))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_47]),c_0_47]) ).
fof(c_0_111,plain,
! [X1903,X1904] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1904,tc_HOL_Obool)),X1903),X1903) = X1903,
inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).
cnf(c_0_112,plain,
( hBOOL(c_fNot)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_81])]) ).
cnf(c_0_113,plain,
hBOOL(hAPP(c_fNot,esk79_1(c_fNot))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_66]),c_0_60]),c_0_60]),c_0_67]) ).
cnf(c_0_114,hypothesis,
( hBOOL(X1)
| hBOOL(c_Int_Onumber__class_Onumber__of(tc_Int_Oint))
| esk79_1(X1) = hAPP(v_Procs,v_pn) ),
inference(spm,[status(thm)],[c_0_108,c_0_87]) ).
cnf(c_0_115,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_116,hypothesis,
hAPP(hAPP(c_Set_Oinsert(X1),v_pn),v_Procs) = v_Procs,
inference(spm,[status(thm)],[c_0_46,c_0_76]) ).
cnf(c_0_117,plain,
( ~ hBOOL(X3)
| ~ hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_110,c_0_88]) ).
cnf(c_0_118,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_119,hypothesis,
( hBOOL(c_fNot)
| hAPP(c_fNot,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_fNot,hAPP(v_Procs,v_pn)) ),
inference(spm,[status(thm)],[c_0_100,c_0_112]) ).
cnf(c_0_120,hypothesis,
( hBOOL(c_fNot)
| hBOOL(c_Int_Onumber__class_Onumber__of(tc_Int_Oint)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_86]) ).
cnf(c_0_121,plain,
( hAPP(hAPP(esk79_1(c_fNot),X2),X3) != X3
| hBOOL(c_List_Olist_OCons(X1)) ),
inference(spm,[status(thm)],[c_0_115,c_0_81]) ).
cnf(c_0_122,hypothesis,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != v_Procs,
inference(spm,[status(thm)],[c_0_59,c_0_116]) ).
cnf(c_0_123,plain,
( ~ hBOOL(X2)
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_88]),c_0_118]) ).
cnf(c_0_124,hypothesis,
( hBOOL(c_fNot)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(v_Procs,v_pn) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_119]),c_0_103]) ).
cnf(c_0_125,hypothesis,
( hBOOL(c_fNot)
| hAPP(c_fNot,c_Int_Onumber__class_Onumber__of(tc_Int_Oint)) = hAPP(c_fNot,hAPP(v_Procs,v_pn)) ),
inference(spm,[status(thm)],[c_0_100,c_0_120]) ).
cnf(c_0_126,plain,
( hAPP(hAPP(X2,X3),X4) != X4
| hBOOL(X2)
| hBOOL(c_List_Olist_OCons(X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_87]),c_0_72]) ).
cnf(c_0_127,hypothesis,
( esk79_1(c_fNot) != v_Procs
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_122,c_0_81]) ).
cnf(c_0_128,hypothesis,
( ~ hBOOL(X1)
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint) != hAPP(v_Procs,v_pn)
| hBOOL(c_fNot) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_129,hypothesis,
( hBOOL(c_fNot)
| c_Int_Onumber__class_Onumber__of(tc_Int_Oint) = hAPP(v_Procs,v_pn) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_125]),c_0_103]) ).
cnf(c_0_130,plain,
( hAPP(X2,X3) != X3
| hBOOL(c_fNot)
| hBOOL(c_List_Olist_OCons(X1)) ),
inference(spm,[status(thm)],[c_0_126,c_0_103]) ).
fof(c_0_131,plain,
! [X123] : X123 != hAPP(c_Nat_OSuc,X123),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_132,hypothesis,
( hBOOL(v_Procs)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_81])]) ).
cnf(c_0_133,hypothesis,
( ~ hBOOL(X1)
| hBOOL(c_fNot) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_134,plain,
( hBOOL(c_fNot)
| hBOOL(c_List_Olist_OCons(X1)) ),
inference(spm,[status(thm)],[c_0_130,c_0_88]) ).
fof(c_0_135,plain,
! [X2150] : X2150 != hAPP(c_Nat_OSuc,X2150),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_131])]) ).
cnf(c_0_136,hypothesis,
( hBOOL(v_Procs)
| hAPP(c_fNot,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_fNot,hAPP(v_Procs,v_pn)) ),
inference(spm,[status(thm)],[c_0_100,c_0_132]) ).
cnf(c_0_137,hypothesis,
hBOOL(c_fNot),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_138,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_139,hypothesis,
( hBOOL(v_Procs)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(v_Procs,v_pn) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_136]),c_0_103]) ).
cnf(c_0_140,hypothesis,
hAPP(c_fNot,hAPP(v_Procs,v_pn)) = hAPP(c_fNot,c_fNot),
inference(spm,[status(thm)],[c_0_100,c_0_137]) ).
cnf(c_0_141,plain,
hBOOL(hAPP(c_Nat_OSuc,esk79_1(c_fNot))),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_81])]) ).
cnf(c_0_142,hypothesis,
esk79_1(c_fNot) = hAPP(c_fNot,hAPP(v_Procs,v_pn)),
inference(spm,[status(thm)],[c_0_72,c_0_94]) ).
cnf(c_0_143,hypothesis,
( hAPP(v_Procs,v_pn) != c_fNot
| hBOOL(v_Procs) ),
inference(spm,[status(thm)],[c_0_67,c_0_139]) ).
cnf(c_0_144,hypothesis,
hAPP(v_Procs,v_pn) = c_fNot,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_140]),c_0_103]) ).
cnf(c_0_145,plain,
hAPP(hAPP(c_Set_Oinsert(X1),hAPP(c_fNot,hAPP(v_Procs,v_pn))),c_Nat_OSuc) = c_Nat_OSuc,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_141]),c_0_142]) ).
cnf(c_0_146,hypothesis,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = hAPP(c_fNot,c_fNot) ),
inference(rw,[status(thm)],[c_0_100,c_0_140]) ).
cnf(c_0_147,hypothesis,
hBOOL(v_Procs),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144])]) ).
cnf(c_0_148,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Nat_OSuc,
inference(spm,[status(thm)],[c_0_59,c_0_145]) ).
cnf(c_0_149,hypothesis,
hAPP(c_fNot,v_Procs) = hAPP(c_fNot,c_fNot),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_150,plain,
( hBOOL(c_Nat_OSuc)
| hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_87])]) ).
cnf(c_0_151,hypothesis,
v_Procs = c_fNot,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_149]),c_0_103]) ).
cnf(c_0_152,hypothesis,
( hBOOL(c_Nat_OSuc)
| hAPP(c_fNot,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_fNot,hAPP(v_Procs,v_pn)) ),
inference(spm,[status(thm)],[c_0_100,c_0_150]) ).
fof(c_0_153,plain,
! [X124] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X124),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
cnf(c_0_154,hypothesis,
hAPP(c_fNot,v_pn) = c_fNot,
inference(rw,[status(thm)],[c_0_144,c_0_151]) ).
cnf(c_0_155,hypothesis,
( hBOOL(c_Nat_OSuc)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(v_Procs,v_pn) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_152]),c_0_103]) ).
fof(c_0_156,plain,
! [X2361,X2362] :
( X2361 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2362),X2361) != X2362 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
fof(c_0_157,plain,
! [X2179,X2180] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2180),hAPP(c_Nat_OSuc,X2179)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2180),X2179)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(c_0_158,plain,
! [X2258] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2258),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_153])]) ).
cnf(c_0_159,hypothesis,
hAPP(c_fNot,c_fNot) = v_pn,
inference(spm,[status(thm)],[c_0_103,c_0_154]) ).
cnf(c_0_160,hypothesis,
( hAPP(v_Procs,v_pn) != c_fNot
| hBOOL(c_Nat_OSuc) ),
inference(spm,[status(thm)],[c_0_67,c_0_155]) ).
cnf(c_0_161,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_162,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_163,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_164,hypothesis,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = v_pn ),
inference(rw,[status(thm)],[c_0_146,c_0_159]) ).
cnf(c_0_165,hypothesis,
hBOOL(c_Nat_OSuc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_144])]) ).
cnf(c_0_166,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]) ).
fof(c_0_167,plain,
! [X2365] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2365),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2365,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
cnf(c_0_168,hypothesis,
hAPP(c_fNot,c_Nat_OSuc) = v_pn,
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_169,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
inference(spm,[status(thm)],[c_0_166,c_0_162]) ).
cnf(c_0_170,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_167]) ).
cnf(c_0_171,hypothesis,
c_fNot = c_Nat_OSuc,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_168]),c_0_154]) ).
cnf(c_0_172,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_173,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_171]),c_0_171]),c_0_172]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW303+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 09:46:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 192.18/34.25 % Version: 3.5.1
% 192.18/34.25 % Preprocessing class: FMLMSMSMSSSNFFN.
% 192.18/34.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 192.18/34.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 192.18/34.25 % Starting new_bool_3 with 300s (1) cores
% 192.18/34.25 % Starting new_bool_1 with 300s (1) cores
% 192.18/34.25 % Starting sh5l with 300s (1) cores
% 192.18/34.25 % new_bool_3 with pid 3152160 completed with status 0
% 192.18/34.25 % Result found by new_bool_3
% 192.18/34.25 % Preprocessing class: FMLMSMSMSSSNFFN.
% 192.18/34.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 192.18/34.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 192.18/34.25 % Starting new_bool_3 with 300s (1) cores
% 192.18/34.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 192.18/34.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 192.18/34.25 % Search class: FGHSM-SSLM32-DFFFFFNN
% 192.18/34.25 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 192.18/34.25 % Starting SubtermCWHack with 28s (1) cores
% 192.18/34.25 % SubtermCWHack with pid 3152164 completed with status 8
% 192.18/34.25 % Starting new_bool_3 with 31s (1) cores
% 192.18/34.25 % new_bool_3 with pid 3152179 completed with status 0
% 192.18/34.25 % Result found by new_bool_3
% 192.18/34.25 % Preprocessing class: FMLMSMSMSSSNFFN.
% 192.18/34.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 192.18/34.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 192.18/34.25 % Starting new_bool_3 with 300s (1) cores
% 192.18/34.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 192.18/34.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 192.18/34.25 % Search class: FGHSM-SSLM32-DFFFFFNN
% 192.18/34.25 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 192.18/34.25 % Starting SubtermCWHack with 28s (1) cores
% 192.18/34.25 % SubtermCWHack with pid 3152164 completed with status 8
% 192.18/34.25 % Starting new_bool_3 with 31s (1) cores
% 192.18/34.25 % Preprocessing time : 0.071 s
% 192.18/34.25 % Presaturation interreduction done
% 192.18/34.25
% 192.18/34.25 % Proof found!
% 192.18/34.25 % SZS status ContradictoryAxioms
% 192.18/34.25 % SZS output start CNFRefutation
% See solution above
% 192.18/34.25 % Parsed axioms : 5243
% 192.18/34.25 % Removed by relevancy pruning/SinE : 3962
% 192.18/34.25 % Initial clauses : 1877
% 192.18/34.25 % Removed in clause preprocessing : 60
% 192.18/34.25 % Initial clauses in saturation : 1817
% 192.18/34.25 % Processed clauses : 8264
% 192.18/34.25 % ...of these trivial : 236
% 192.18/34.25 % ...subsumed : 3852
% 192.18/34.25 % ...remaining for further processing : 4176
% 192.18/34.25 % Other redundant clauses eliminated : 3214
% 192.18/34.25 % Clauses deleted for lack of memory : 0
% 192.18/34.25 % Backward-subsumed : 150
% 192.18/34.25 % Backward-rewritten : 751
% 192.18/34.25 % Generated clauses : 110539
% 192.18/34.25 % ...of the previous two non-redundant : 101632
% 192.18/34.25 % ...aggressively subsumed : 0
% 192.18/34.25 % Contextual simplify-reflections : 16
% 192.18/34.25 % Paramodulations : 107282
% 192.18/34.25 % Factorizations : 12
% 192.18/34.25 % NegExts : 0
% 192.18/34.25 % Equation resolutions : 3257
% 192.18/34.25 % Disequality decompositions : 0
% 192.18/34.25 % Total rewrite steps : 24910
% 192.18/34.25 % ...of those cached : 18646
% 192.18/34.25 % Propositional unsat checks : 0
% 192.18/34.25 % Propositional check models : 0
% 192.18/34.25 % Propositional check unsatisfiable : 0
% 192.18/34.25 % Propositional clauses : 0
% 192.18/34.25 % Propositional clauses after purity: 0
% 192.18/34.25 % Propositional unsat core size : 0
% 192.18/34.25 % Propositional preprocessing time : 0.000
% 192.18/34.25 % Propositional encoding time : 0.000
% 192.18/34.25 % Propositional solver time : 0.000
% 192.18/34.25 % Success case prop preproc time : 0.000
% 192.18/34.25 % Success case prop encoding time : 0.000
% 192.18/34.25 % Success case prop solver time : 0.000
% 192.18/34.25 % Current number of processed clauses : 1770
% 192.18/34.25 % Positive orientable unit clauses : 458
% 192.18/34.25 % Positive unorientable unit clauses: 45
% 192.18/34.25 % Negative unit clauses : 226
% 192.18/34.25 % Non-unit-clauses : 1041
% 192.18/34.25 % Current number of unprocessed clauses: 93734
% 192.18/34.25 % ...number of literals in the above : 233715
% 192.18/34.25 % Current number of archived formulas : 0
% 192.18/34.25 % Current number of archived clauses : 2258
% 192.18/34.25 % Clause-clause subsumption calls (NU) : 340469
% 192.18/34.25 % Rec. Clause-clause subsumption calls : 224151
% 192.18/34.25 % Non-unit clause-clause subsumptions : 2400
% 192.18/34.25 % Unit Clause-clause subsumption calls : 29865
% 192.18/34.25 % Rewrite failures with RHS unbound : 203
% 192.18/34.25 % BW rewrite match attempts : 6810
% 192.18/34.25 % BW rewrite match successes : 627
% 192.18/34.25 % Condensation attempts : 0
% 192.18/34.25 % Condensation successes : 0
% 192.18/34.25 % Termbank termtop insertions : 2670048
% 192.18/34.25 % Search garbage collected termcells : 59977
% 192.18/34.25
% 192.18/34.25 % -------------------------------------------------
% 192.18/34.25 % User time : 32.108 s
% 192.18/34.25 % System time : 1.142 s
% 192.18/34.25 % Total time : 33.250 s
% 192.18/34.25 % Maximum resident set size: 16260 pages
% 192.18/34.25
% 192.18/34.25 % -------------------------------------------------
% 192.18/34.25 % User time : 32.376 s
% 192.18/34.25 % System time : 1.159 s
% 192.18/34.25 % Total time : 33.534 s
% 192.18/34.25 % Maximum resident set size: 12288 pages
% 192.18/34.25 % E exiting
%------------------------------------------------------------------------------