%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW367+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 : n009.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 03:12:02 PM UTC 2026
% Result : ContradictoryAxioms 104.32s 18.58s
% Output : CNFRefutation 104.32s
% 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,
! [X42,X9] :
( hAPP(c_Set_OCollect(X9),X42) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X42,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X9] : c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X9),hAPP(c_COMBK(tc_HOL_Obool,X9),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X42,X9] : hAPP(c_Set_OCollect(X9),X42) = X42,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X42,X9] : hAPP(c_Set_OCollect(X9),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9),c_fNot),X42)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),hAPP(c_Set_OCollect(X9),X42)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X42,X2,X7,X9] : hAPP(c_Set_Ovimage(X9,X7,X2),hAPP(c_Set_OCollect(X7),X42)) = hAPP(c_Set_OCollect(X9),hAPP(hAPP(c_COMBB(X7,tc_HOL_Obool,X9),X42),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(help_c__COMBK__1,axiom,
! [X280,X279,X9,X25] : hAPP(hAPP(c_COMBK(X25,X9),X279),X280) = X279,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Zero__neq__Suc,axiom,
! [X22] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X11,X9] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),X11)) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_vimage__id,axiom,
! [X11,X9] : hAPP(c_Set_Ovimage(X9,X9,c_Fun_Oid(X9)),X11) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(help_c__fNot__1,axiom,
! [X42] :
( ~ hBOOL(X42)
| ~ hBOOL(hAPP(c_fNot,X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_UNIV__def,axiom,
! [X9] : c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X9),hAPP(c_COMBK(tc_HOL_Obool,X9),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,
! [X9] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_add__0__iff,axiom,
! [X12,X13,X9] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X9)
=> ( X13 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X13),X12)
<=> X12 = c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X23,X22] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),hAPP(c_Nat_OSuc,X23)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_id__def,axiom,
! [X176,X25] : hAPP(c_Fun_Oid(X25),X176) = X176,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).
fof(help_c__COMBB__1,axiom,
! [X27,X41,X42,X18,X9,X7] : hAPP(hAPP(hAPP(c_COMBB(X7,X9,X18),X42),X41),X27) = hAPP(X42,hAPP(X41,X27)),
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,
! [X22] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X23] : X23 != hAPP(c_Nat_OSuc,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_21,plain,
! [X42,X9] :
( hAPP(c_Set_OCollect(X9),X42) = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X42,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_22,plain,
! [X9848] : c_Orderings_Obot__class_Obot(tc_fun(X9848,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X9848),hAPP(c_COMBK(tc_HOL_Obool,X9848),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_23,plain,
! [X9840,X9841] : hAPP(c_Set_OCollect(X9841),X9840) = X9840,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_24,plain,
! [X9823,X9824] : hAPP(c_Set_OCollect(X9824),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9824),c_fNot),X9823)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9824,tc_HOL_Obool)),hAPP(c_Set_OCollect(X9824),X9823)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_25,plain,
! [X9853,X9854,X9855,X9856] : hAPP(c_Set_Ovimage(X9856,X9855,X9854),hAPP(c_Set_OCollect(X9855),X9853)) = hAPP(c_Set_OCollect(X9856),hAPP(hAPP(c_COMBB(X9855,tc_HOL_Obool,X9856),X9853),X9854)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_26,plain,
! [X9834,X9835,X9836,X9837,X9839] :
( ( hAPP(c_Set_OCollect(X9839),X9837) = c_Orderings_Obot__class_Obot(tc_fun(X9839,tc_HOL_Obool))
| hBOOL(hAPP(X9837,esk250_1(X9837))) )
& ( ~ hBOOL(hAPP(X9834,X9836))
| hAPP(c_Set_OCollect(X9835),X9834) != c_Orderings_Obot__class_Obot(tc_fun(X9835,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,
! [X17461,X17462,X17463,X17464] : hAPP(hAPP(c_COMBK(X17464,X17463),X17462),X17461) = X17462,
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,
! [X22] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X22),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_31,plain,
! [X4112,X4113] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4113,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4113,tc_HOL_Obool)),X4112)) = X4112,
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,
! [X10040,X10041] : hAPP(c_Set_Ovimage(X10041,X10041,c_Fun_Oid(X10041)),X10040) = X10040,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
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,
! [X42] :
( ~ hBOOL(X42)
| ~ hBOOL(hAPP(c_fNot,X42)) ),
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,esk250_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,
! [X9852] : c_Orderings_Otop__class_Otop(tc_fun(X9852,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X9852),hAPP(c_COMBK(tc_HOL_Obool,X9852),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_40,plain,
! [X1908] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1908),
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_Fun_Oid(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,
! [X17487] :
( ~ hBOOL(X17487)
| ~ hBOOL(hAPP(c_fNot,X17487)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
cnf(c_0_48,plain,
( hBOOL(hAPP(X1,esk250_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,
! [X9087] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9087,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9087,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9087,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,
! [X2127,X2128,X2129] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2129)
| X2128 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2129),X2128),X2127)
| X2127 != c_Groups_Ozero__class_Ozero(X2129) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2129)
| X2127 = c_Groups_Ozero__class_Ozero(X2129)
| X2128 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2129),X2128),X2127) ) ),
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,
! [X1307,X1308] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1308),hAPP(c_Nat_OSuc,X1307)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1308),X1307)),
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,
! [X10044,X10045] : hAPP(c_Fun_Oid(X10045),X10044) = X10044,
inference(variable_rename,[status(thm)],[fact_id__def]) ).
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_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_59,plain,
! [X17465,X17466,X17467,X17468,X17469,X17470] : hAPP(hAPP(hAPP(c_COMBB(X17470,X17469,X17468),X17467),X17466),X17465) = hAPP(X17467,hAPP(X17466,X17465)),
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,
! [X1923] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1923),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1923,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_69,plain,
! [X23] : X23 != hAPP(c_Nat_OSuc,X23),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_70,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_71,plain,
c_Fun_Oid(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,
! [X581] : X581 != hAPP(c_Nat_OSuc,X581),
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
% 0.00/0.04 % Problem : SWW367+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.52 % Computer : n009.cluster.edu
% 0.20/0.52 % Model : x86_64 x86_64
% 0.20/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.52 % Memory : 8046.5625MB
% 0.20/0.52 % OS : Linux 6.8.0-71-generic
% 0.20/0.52 % CPULimit : 300
% 0.20/0.52 % WCLimit : 300
% 0.20/0.52 % DateTime : Mon Sep 21 09:49:58 UTC 2026
% 0.20/0.53 % CPUTime :
% 0.20/0.53 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.60 Running first-order theorem proving
% 0.20/0.60 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
% 104.32/18.58 % Version: 3.5.1
% 104.32/18.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 104.32/18.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.32/18.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.32/18.58 % Starting new_bool_3 with 300s (1) cores
% 104.32/18.58 % Starting new_bool_1 with 300s (1) cores
% 104.32/18.58 % Starting sh5l with 300s (1) cores
% 104.32/18.58 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1453243 completed with status 0
% 104.32/18.58 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 104.32/18.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 104.32/18.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.32/18.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.32/18.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 104.32/18.58 % No SInE strategy applied
% 104.32/18.58 % Search class: FGHSM-SMLM33-DFFFFFNN
% 104.32/18.58 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 104.32/18.58 % Starting SubtermCWHack with 135s (1) cores
% 104.32/18.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 104.32/18.58 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 104.32/18.58 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 104.32/18.58 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 104.32/18.58 % SAT001_CA_MinMin_p005000_rr with pid 1453254 completed with status 0
% 104.32/18.58 % Result found by SAT001_CA_MinMin_p005000_rr
% 104.32/18.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 104.32/18.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.32/18.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.32/18.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 104.32/18.58 % No SInE strategy applied
% 104.32/18.58 % Search class: FGHSM-SMLM33-DFFFFFNN
% 104.32/18.58 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 104.32/18.58 % Starting SubtermCWHack with 135s (1) cores
% 104.32/18.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 104.32/18.58 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 104.32/18.58 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 104.32/18.58 % Preprocessing time : 0.189 s
% 104.32/18.58 % Presaturation interreduction done
% 104.32/18.58
% 104.32/18.58 % Proof found!
% 104.32/18.58 % SZS status ContradictoryAxioms
% 104.32/18.58 % SZS output start CNFRefutation
% See solution above
% 104.32/18.58 % Parsed axioms : 5230
% 104.32/18.58 % Removed by relevancy pruning/SinE : 0
% 104.32/18.58 % Initial clauses : 7605
% 104.32/18.58 % Removed in clause preprocessing : 245
% 104.32/18.58 % Initial clauses in saturation : 7360
% 104.32/18.58 % Processed clauses : 22844
% 104.32/18.58 % ...of these trivial : 572
% 104.32/18.58 % ...subsumed : 7803
% 104.32/18.58 % ...remaining for further processing : 14469
% 104.32/18.58 % Other redundant clauses eliminated : 1467
% 104.32/18.58 % Clauses deleted for lack of memory : 0
% 104.32/18.58 % Backward-subsumed : 209
% 104.32/18.58 % Backward-rewritten : 558
% 104.32/18.58 % Generated clauses : 286513
% 104.32/18.58 % ...of the previous two non-redundant : 274848
% 104.32/18.58 % ...aggressively subsumed : 0
% 104.32/18.58 % Contextual simplify-reflections : 31
% 104.32/18.58 % Paramodulations : 285073
% 104.32/18.58 % Factorizations : 8
% 104.32/18.58 % NegExts : 0
% 104.32/18.58 % Equation resolutions : 1498
% 104.32/18.58 % Disequality decompositions : 0
% 104.32/18.58 % Total rewrite steps : 66043
% 104.32/18.58 % ...of those cached : 48263
% 104.32/18.58 % Propositional unsat checks : 3
% 104.32/18.58 % Propositional check models : 2
% 104.32/18.58 % Propositional check unsatisfiable : 0
% 104.32/18.58 % Propositional clauses : 0
% 104.32/18.58 % Propositional clauses after purity: 0
% 104.32/18.58 % Propositional unsat core size : 0
% 104.32/18.58 % Propositional preprocessing time : 0.000
% 104.32/18.58 % Propositional encoding time : 0.197
% 104.32/18.58 % Propositional solver time : 0.100
% 104.32/18.58 % Success case prop preproc time : 0.000
% 104.32/18.58 % Success case prop encoding time : 0.000
% 104.32/18.58 % Success case prop solver time : 0.000
% 104.32/18.58 % Current number of processed clauses : 7258
% 104.32/18.58 % Positive orientable unit clauses : 1760
% 104.32/18.58 % Positive unorientable unit clauses: 126
% 104.32/18.58 % Negative unit clauses : 1139
% 104.32/18.58 % Non-unit-clauses : 4233
% 104.32/18.58 % Current number of unprocessed clauses: 235720
% 104.32/18.58 % ...number of literals in the above : 456795
% 104.32/18.58 % Current number of archived formulas : 0
% 104.32/18.58 % Current number of archived clauses : 6750
% 104.32/18.58 % Clause-clause subsumption calls (NU) : 5449230
% 104.32/18.58 % Rec. Clause-clause subsumption calls : 2591337
% 104.32/18.58 % Non-unit clause-clause subsumptions : 7778
% 104.32/18.58 % Unit Clause-clause subsumption calls : 320456
% 104.32/18.58 % Rewrite failures with RHS unbound : 246
% 104.32/18.58 % BW rewrite match attempts : 40691
% 104.32/18.58 % BW rewrite match successes : 1322
% 104.32/18.58 % Condensation attempts : 310474
% 104.32/18.58 % Condensation successes : 2670
% 104.32/18.58 % Termbank termtop insertions : 8461648
% 104.32/18.58 % Search garbage collected termcells : 102629
% 104.32/18.58
% 104.32/18.58 % -------------------------------------------------
% 104.32/18.58 % User time : 14.497 s
% 104.32/18.58 % System time : 0.464 s
% 104.32/18.58 % Total time : 14.961 s
% 104.32/18.58 % Maximum resident set size: 42592 pages
% 104.32/18.58
% 104.32/18.58 % -------------------------------------------------
% 104.32/18.58 % User time : 68.319 s
% 104.32/18.58 % System time : 1.999 s
% 104.32/18.58 % Total time : 70.319 s
% 104.32/18.58 % Maximum resident set size: 12032 pages
% 104.32/18.58 % E exiting
%------------------------------------------------------------------------------