%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW363+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 : n002.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 03:10:23 PM UTC 2026
% Result : ContradictoryAxioms 102.64s 22.26s
% Output : CNFRefutation 102.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 90 ( 74 unt; 0 def)
% Number of atoms : 114 ( 91 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 56 ( 32 ~; 18 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 155 ( 17 sgn 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X44,X10] :
( hAPP(c_Set_OCollect(X10),X44) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X44,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X10] : c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X44,X10] : hAPP(c_Set_OCollect(X10),X44) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X44,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X44)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X44,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(c_Set_OCollect(X8),X44)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(X8,tc_HOL_Obool,X10),X44),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(help_c__COMBK__1,axiom,
! [X280,X279,X10,X36] : hAPP(hAPP(c_COMBK(X36,X10),X279),X280) = X279,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Zero__not__Suc,axiom,
! [X16] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X11,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X11)) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_vimage__ident,axiom,
! [X60,X10] : hAPP(c_Set_Ovimage(X10,X10,c_COMBI(X10)),X60) = X60,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__ident) ).
fof(help_c__fNot__1,axiom,
! [X44] :
( ~ hBOOL(X44)
| ~ hBOOL(hAPP(c_fNot,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_UNIV__def,axiom,
! [X10] : c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_Compl__empty__eq,axiom,
! [X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_add__0__iff,axiom,
! [X12,X28,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( X28 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X28),X12)
<=> X12 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X17,X16] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),hAPP(c_Nat_OSuc,X17)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(help_c__COMBI__1,axiom,
! [X279,X36] : hAPP(c_COMBI(X36),X279) = X279,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(help_c__COMBB__1,axiom,
! [X43,X50,X44,X27,X10,X8] : hAPP(hAPP(hAPP(c_COMBB(X8,X10,X27),X44),X50),X43) = hAPP(X44,hAPP(X50,X43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X16] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X17] : X17 != hAPP(c_Nat_OSuc,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_21,plain,
! [X44,X10] :
( hAPP(c_Set_OCollect(X10),X44) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X44,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_22,plain,
! [X11047] : c_Orderings_Obot__class_Obot(tc_fun(X11047,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11047),hAPP(c_COMBK(tc_HOL_Obool,X11047),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_23,plain,
! [X11027,X11028] : hAPP(c_Set_OCollect(X11028),X11027) = X11027,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_24,plain,
! [X11070,X11071] : hAPP(c_Set_OCollect(X11071),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11071),c_fNot),X11070)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11071,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11071),X11070)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_25,plain,
! [X11066,X11067,X11068,X11069] : hAPP(c_Set_Ovimage(X11069,X11068,X11067),hAPP(c_Set_OCollect(X11068),X11066)) = hAPP(c_Set_OCollect(X11069),hAPP(hAPP(c_COMBB(X11068,tc_HOL_Obool,X11069),X11066),X11067)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_26,plain,
! [X11041,X11042,X11043,X11044,X11046] :
( ( hAPP(c_Set_OCollect(X11046),X11044) = c_Orderings_Obot__class_Obot(tc_fun(X11046,tc_HOL_Obool))
| hBOOL(hAPP(X11044,esk279_1(X11044))) )
& ( ~ hBOOL(hAPP(X11041,X11043))
| hAPP(c_Set_OCollect(X11042),X11041) != c_Orderings_Obot__class_Obot(tc_fun(X11042,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_21])])])])])]) ).
fof(c_0_27,plain,
! [X17462,X17463,X17464,X17465] : hAPP(hAPP(c_COMBK(X17465,X17464),X17463),X17462) = X17463,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_28,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X16] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X16),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_31,plain,
! [X4481,X4482] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4482,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4482,tc_HOL_Obool)),X4481)) = X4481,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_32,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_24]) ).
fof(c_0_33,plain,
! [X10229,X10230] : hAPP(c_Set_Ovimage(X10230,X10230,c_COMBI(X10230)),X10229) = X10229,
inference(variable_rename,[status(thm)],[fact_vimage__ident]) ).
cnf(c_0_34,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_35,plain,
! [X44] :
( ~ hBOOL(X44)
| ~ hBOOL(hAPP(c_fNot,X44)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_36,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk279_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_39,plain,
! [X11054] : c_Orderings_Otop__class_Otop(tc_fun(X11054,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11054),hAPP(c_COMBK(tc_HOL_Obool,X11054),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_40,plain,
! [X1698] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1698),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_41,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_42,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
cnf(c_0_43,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_31]) ).
cnf(c_0_44,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_32,c_0_29]),c_0_29]) ).
cnf(c_0_45,plain,
hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_46,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_29]),c_0_29]) ).
fof(c_0_47,plain,
! [X17488] :
( ~ hBOOL(X17488)
| ~ hBOOL(hAPP(c_fNot,X17488)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
cnf(c_0_48,plain,
( hBOOL(hAPP(X1,esk279_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_36,c_0_29]) ).
cnf(c_0_49,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_50,plain,
! [X9624] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9624,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9624,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9624,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_51,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_52,plain,
! [X1976,X1977,X1978] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1978)
| X1977 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1978),X1977),X1976)
| X1976 != c_Groups_Ozero__class_Ozero(X1978) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1978)
| X1976 = c_Groups_Ozero__class_Ozero(X1978)
| X1977 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1978),X1977),X1976) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])]) ).
fof(c_0_53,plain,
! [X1301,X1302] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1302),hAPP(c_Nat_OSuc,X1301)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1302),X1301)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_54,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_55,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_56,plain,
! [X17460,X17461] : hAPP(c_COMBI(X17461),X17460) = X17460,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
cnf(c_0_57,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_43,c_0_44]),c_0_44]) ).
cnf(c_0_58,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_COMBI(X1)) = X2,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_59,plain,
! [X17466,X17467,X17468,X17469,X17470,X17471] : hAPP(hAPP(hAPP(c_COMBB(X17471,X17470,X17469),X17468),X17467),X17466) = hAPP(X17468,hAPP(X17467,X17466)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_60,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_61,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_48]),c_0_49]),c_0_37]) ).
cnf(c_0_62,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_50]) ).
cnf(c_0_63,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_51,c_0_29]) ).
cnf(c_0_64,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,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_53]) ).
cnf(c_0_66,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(c_0_67,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_68,plain,
! [X1711] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1711),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1711,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_69,plain,
! [X17] : X17 != hAPP(c_Nat_OSuc,X17),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_70,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_71,plain,
c_COMBI(tc_HOL_Obool) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_72,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_73,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_74,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_62,c_0_44]) ).
cnf(c_0_75,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_37,c_0_63]) ).
cnf(c_0_76,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_55]),c_0_66])]),c_0_67]) ).
cnf(c_0_77,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_68]) ).
fof(c_0_78,plain,
! [X344] : X344 != hAPP(c_Nat_OSuc,X344),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_69])]) ).
cnf(c_0_79,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_80,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_73,c_0_61]) ).
cnf(c_0_81,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_74]),c_0_75]),c_0_49]) ).
cnf(c_0_82,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_76,c_0_65]) ).
cnf(c_0_83,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls)) = X1,
inference(rw,[status(thm)],[c_0_77,c_0_55]) ).
cnf(c_0_84,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_85,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_86,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_88,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_89,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_85]),c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW363+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 % Computer : n002.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.42 % WCLimit : 300
% 0.13/5.42 % DateTime : Mon Sep 21 09:51:52 UTC 2026
% 0.13/5.42 % CPUTime :
% 0.13/5.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.49 Running first-order theorem proving
% 0.13/5.50 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
% 102.64/22.26 % Version: 3.5.1
% 102.64/22.26 % Preprocessing class: FMLMSMSMSSSNFFN.
% 102.64/22.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.64/22.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 102.64/22.26 % Starting new_bool_3 with 300s (1) cores
% 102.64/22.26 % Starting new_bool_1 with 300s (1) cores
% 102.64/22.26 % Starting sh5l with 300s (1) cores
% 102.64/22.26 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3005232 completed with status 0
% 102.64/22.26 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 102.64/22.26 % Preprocessing class: FMLMSMSMSSSNFFN.
% 102.64/22.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.64/22.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 102.64/22.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 102.64/22.26 % No SInE strategy applied
% 102.64/22.26 % Search class: FGHSM-SMLM33-DFFFFFNN
% 102.64/22.26 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 102.64/22.26 % Starting SubtermCWHack with 135s (1) cores
% 102.64/22.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 102.64/22.26 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 102.64/22.26 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 102.64/22.26 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 102.64/22.26 % SAT001_CA_MinMin_p005000_rr with pid 3005242 completed with status 0
% 102.64/22.26 % Result found by SAT001_CA_MinMin_p005000_rr
% 102.64/22.26 % Preprocessing class: FMLMSMSMSSSNFFN.
% 102.64/22.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.64/22.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 102.64/22.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 102.64/22.26 % No SInE strategy applied
% 102.64/22.26 % Search class: FGHSM-SMLM33-DFFFFFNN
% 102.64/22.26 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 102.64/22.26 % Starting SubtermCWHack with 135s (1) cores
% 102.64/22.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 102.64/22.26 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 102.64/22.26 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 102.64/22.26 % Preprocessing time : 0.309 s
% 102.64/22.26 % Presaturation interreduction done
% 102.64/22.26
% 102.64/22.26 % Proof found!
% 102.64/22.26 % SZS status ContradictoryAxioms
% 102.64/22.26 % SZS output start CNFRefutation
% See solution above
% 102.64/22.26 % Parsed axioms : 5229
% 102.64/22.26 % Removed by relevancy pruning/SinE : 0
% 102.64/22.26 % Initial clauses : 7605
% 102.64/22.26 % Removed in clause preprocessing : 245
% 102.64/22.26 % Initial clauses in saturation : 7360
% 102.64/22.26 % Processed clauses : 21692
% 102.64/22.26 % ...of these trivial : 522
% 102.64/22.26 % ...subsumed : 7727
% 102.64/22.26 % ...remaining for further processing : 13443
% 102.64/22.26 % Other redundant clauses eliminated : 1287
% 102.64/22.26 % Clauses deleted for lack of memory : 0
% 102.64/22.26 % Backward-subsumed : 217
% 102.64/22.26 % Backward-rewritten : 546
% 102.64/22.26 % Generated clauses : 215348
% 102.64/22.26 % ...of the previous two non-redundant : 206275
% 102.64/22.26 % ...aggressively subsumed : 0
% 102.64/22.26 % Contextual simplify-reflections : 31
% 102.64/22.26 % Paramodulations : 214094
% 102.64/22.26 % Factorizations : 2
% 102.64/22.26 % NegExts : 0
% 102.64/22.26 % Equation resolutions : 1318
% 102.64/22.26 % Disequality decompositions : 0
% 102.64/22.26 % Total rewrite steps : 58307
% 102.64/22.26 % ...of those cached : 40978
% 102.64/22.26 % Propositional unsat checks : 3
% 102.64/22.26 % Propositional check models : 2
% 102.64/22.26 % Propositional check unsatisfiable : 0
% 102.64/22.26 % Propositional clauses : 0
% 102.64/22.26 % Propositional clauses after purity: 0
% 102.64/22.26 % Propositional unsat core size : 0
% 102.64/22.26 % Propositional preprocessing time : 0.000
% 102.64/22.26 % Propositional encoding time : 0.243
% 102.64/22.26 % Propositional solver time : 0.114
% 102.64/22.26 % Success case prop preproc time : 0.000
% 102.64/22.26 % Success case prop encoding time : 0.000
% 102.64/22.26 % Success case prop solver time : 0.000
% 102.64/22.26 % Current number of processed clauses : 6237
% 102.64/22.26 % Positive orientable unit clauses : 1667
% 102.64/22.26 % Positive unorientable unit clauses: 127
% 102.64/22.26 % Negative unit clauses : 747
% 102.64/22.26 % Non-unit-clauses : 3696
% 102.64/22.26 % Current number of unprocessed clauses: 177308
% 102.64/22.26 % ...number of literals in the above : 327651
% 102.64/22.26 % Current number of archived formulas : 0
% 102.64/22.26 % Current number of archived clauses : 6745
% 102.64/22.26 % Clause-clause subsumption calls (NU) : 6465211
% 102.64/22.26 % Rec. Clause-clause subsumption calls : 3480811
% 102.64/22.26 % Non-unit clause-clause subsumptions : 7572
% 102.64/22.26 % Unit Clause-clause subsumption calls : 285007
% 102.64/22.26 % Rewrite failures with RHS unbound : 478
% 102.64/22.26 % BW rewrite match attempts : 41173
% 102.64/22.26 % BW rewrite match successes : 1411
% 102.64/22.26 % Condensation attempts : 238135
% 102.64/22.26 % Condensation successes : 2132
% 102.64/22.26 % Termbank termtop insertions : 7268166
% 102.64/22.26 % Search garbage collected termcells : 102651
% 102.64/22.26
% 102.64/22.26 % -------------------------------------------------
% 102.64/22.26 % User time : 14.940 s
% 102.64/22.26 % System time : 0.395 s
% 102.64/22.26 % Total time : 15.335 s
% 102.64/22.26 % Maximum resident set size: 42588 pages
% 102.64/22.26
% 102.64/22.26 % -------------------------------------------------
% 102.64/22.26 % User time : 67.844 s
% 102.64/22.26 % System time : 1.883 s
% 102.64/22.26 % Total time : 69.727 s
% 102.64/22.26 % Maximum resident set size: 12544 pages
% 102.64/22.26 % E exiting
%------------------------------------------------------------------------------