%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV693-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 02:59:46 PM UTC 2026
% Result : Unsatisfiable 17.05s 3.11s
% Output : CNFRefutation 17.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of clauses : 55 ( 37 unt; 2 nHn; 33 RR)
% Number of literals : 79 ( 36 equ; 33 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 7 con; 0-5 aty)
% Number of variables : 81 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_mult__eq__1__iff_1,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_not__add__less1_0,axiom,
~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
cnf(cls_le__add__diff__inverse_0,axiom,
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
cnf(cls_conjecture_0,negated_conjecture,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_atLeastLessThan__singleton_0,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X1),tc_nat) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__singleton_0) ).
cnf(cls_atLeastLessThan0_0,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan0_0) ).
cnf(cls_add__Suc__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_atLeastSucLessThan__greaterThanLessThan_0,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X1),X2,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
cnf(cls_ivl__disj__un_I17_J_0,axiom,
( ~ hBOOL(hAPP(c_lessequals(X2,X1),X3))
| ~ hBOOL(hAPP(c_lessequals(X3,X1),X4))
| ~ class_Orderings_Olinorder(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
cnf(cls_le__Suc__ex__iff_1,axiom,
hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__ex__iff_1) ).
cnf(cls_assms_0,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_0) ).
cnf(cls_less__Suc__eq__le_0,axiom,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2)))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(cls_not__less__eq__eq_0,axiom,
( hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X1),tc_nat),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
cnf(cls_less__eq__Suc__le__raw_0,axiom,
c_HOL_Oord__class_Oless(v_n,tc_nat) = c_lessequals(hAPP(c_Suc,v_n),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le__raw_0) ).
cnf(c_0_19,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(fof_simplification,[status(thm)],[cls_mult__eq__1__iff_1]) ).
cnf(c_0_20,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I12_J_0]) ).
cnf(c_0_21,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_19 ).
cnf(c_0_22,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2 ),
c_0_20 ).
cnf(c_0_23,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_24,plain,
~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),X1)),
inference(fof_simplification,[status(thm)],[cls_not__add__less1_0]) ).
cnf(c_0_25,plain,
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_le__add__diff__inverse_0]) ).
cnf(c_0_26,negated_conjecture,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_27,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X1),tc_nat) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
cls_atLeastLessThan__singleton_0 ).
cnf(c_0_28,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),
cls_atLeastLessThan0_0 ).
cnf(c_0_29,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc__right_0 ).
cnf(c_0_30,plain,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])])]) ).
cnf(c_0_31,axiom,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
cls_natgb_Oadd__r0__iff_1 ).
cnf(c_0_32,plain,
~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat),X1)),
c_0_24 ).
cnf(c_0_33,plain,
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) = X2 ),
c_0_25 ).
cnf(c_0_34,negated_conjecture,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))),
c_0_26 ).
cnf(c_0_35,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_36,plain,
c_Set_Oinsert(X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X1),tc_nat),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X1),X2,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat),
cls_atLeastSucLessThan__greaterThanLessThan_0 ).
cnf(c_0_38,plain,
( ~ hBOOL(hAPP(c_lessequals(X2,X1),X3))
| ~ hBOOL(hAPP(c_lessequals(X3,X1),X4))
| ~ class_Orderings_Olinorder(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_ivl__disj__un_I17_J_0]) ).
cnf(c_0_39,axiom,
hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))),
cls_le__Suc__ex__iff_1 ).
cnf(c_0_40,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(c_Suc,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_41,plain,
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)),
cls_assms_0 ).
cnf(c_0_43,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2)))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) ),
inference(fof_simplification,[status(thm)],[cls_less__Suc__eq__le_0]) ).
cnf(c_0_44,negated_conjecture,
hAPP(hAPP(c_COMBC(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),tc_nat,tc_nat,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(v_i,hAPP(c_Suc,v_i),tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_i),v_n,tc_nat),tc_fun(tc_nat,tc_bool))),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_nat,tc_nat),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)) != hAPP(hAPP(c_COMBC(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_nat,tc_nat),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_28]),c_0_36]),c_0_37]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_45,plain,
( ~ hBOOL(hAPP(c_lessequals(X2,X1),X3))
| ~ hBOOL(hAPP(c_lessequals(X3,X1),X4))
| ~ class_Orderings_Olinorder(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1),tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1) ),
c_0_38 ).
cnf(c_0_46,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder ).
cnf(c_0_47,plain,
hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(c_Suc,X1))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
~ hBOOL(hAPP(c_lessequals(v_n,tc_nat),v_i)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2)))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) ),
c_0_43 ).
cnf(c_0_50,negated_conjecture,
~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,v_i),tc_nat),v_n)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_51,axiom,
( hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X1),tc_nat),X2)) ),
cls_not__less__eq__eq_0 ).
cnf(c_0_52,axiom,
c_HOL_Oord__class_Oless(v_n,tc_nat) = c_lessequals(hAPP(c_Suc,v_n),tc_nat),
cls_less__eq__Suc__le__raw_0 ).
cnf(c_0_53,plain,
~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_n,tc_nat),hAPP(c_Suc,v_i))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV693-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n020.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 09:20:32 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 17.05/3.11 % Version: 3.5.1
% 17.05/3.11 % Preprocessing class: FMLMSMSMSSSNFFN.
% 17.05/3.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.05/3.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.05/3.11 % Starting new_bool_3 with 300s (1) cores
% 17.05/3.11 % Starting new_bool_1 with 300s (1) cores
% 17.05/3.11 % Starting sh5l with 300s (1) cores
% 17.05/3.11 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2575919 completed with status 0
% 17.05/3.11 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 17.05/3.11 % Preprocessing class: FMLMSMSMSSSNFFN.
% 17.05/3.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.05/3.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.05/3.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.05/3.11 % No SInE strategy applied
% 17.05/3.11 % Search class: FGHSM-SMLM32-DFFFFFNN
% 17.05/3.11 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 17.05/3.11 % Starting SubtermCWHack with 136s (1) cores
% 17.05/3.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 17.05/3.11 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 17.05/3.11 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 17.05/3.11 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 17.05/3.11 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2575930 completed with status 0
% 17.05/3.11 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 17.05/3.11 % Preprocessing class: FMLMSMSMSSSNFFN.
% 17.05/3.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.05/3.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.05/3.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.05/3.11 % No SInE strategy applied
% 17.05/3.11 % Search class: FGHSM-SMLM32-DFFFFFNN
% 17.05/3.11 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 17.05/3.11 % Starting SubtermCWHack with 136s (1) cores
% 17.05/3.11 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 17.05/3.11 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 17.05/3.11 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 17.05/3.11 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 17.05/3.11 % Preprocessing time : 0.037 s
% 17.05/3.11 % Presaturation interreduction done
% 17.05/3.11
% 17.05/3.11 % Proof found!
% 17.05/3.11 % SZS status Unsatisfiable
% 17.05/3.11 % SZS output start CNFRefutation
% See solution above
% 17.05/3.11 % Parsed axioms : 1471
% 17.05/3.11 % Removed by relevancy pruning/SinE : 0
% 17.05/3.11 % Initial clauses : 1471
% 17.05/3.11 % Removed in clause preprocessing : 0
% 17.05/3.11 % Initial clauses in saturation : 1471
% 17.05/3.11 % Processed clauses : 8425
% 17.05/3.11 % ...of these trivial : 204
% 17.05/3.11 % ...subsumed : 5569
% 17.05/3.11 % ...remaining for further processing : 2652
% 17.05/3.11 % Other redundant clauses eliminated : 534
% 17.05/3.11 % Clauses deleted for lack of memory : 0
% 17.05/3.11 % Backward-subsumed : 45
% 17.05/3.11 % Backward-rewritten : 77
% 17.05/3.11 % Generated clauses : 52974
% 17.05/3.11 % ...of the previous two non-redundant : 45522
% 17.05/3.11 % ...aggressively subsumed : 0
% 17.05/3.11 % Contextual simplify-reflections : 5
% 17.05/3.11 % Paramodulations : 52407
% 17.05/3.11 % Factorizations : 4
% 17.05/3.11 % NegExts : 0
% 17.05/3.11 % Equation resolutions : 563
% 17.05/3.11 % Disequality decompositions : 0
% 17.05/3.11 % Total rewrite steps : 35793
% 17.05/3.11 % ...of those cached : 32988
% 17.05/3.11 % Propositional unsat checks : 0
% 17.05/3.11 % Propositional check models : 0
% 17.05/3.11 % Propositional check unsatisfiable : 0
% 17.05/3.11 % Propositional clauses : 0
% 17.05/3.11 % Propositional clauses after purity: 0
% 17.05/3.11 % Propositional unsat core size : 0
% 17.05/3.11 % Propositional preprocessing time : 0.000
% 17.05/3.11 % Propositional encoding time : 0.000
% 17.05/3.11 % Propositional solver time : 0.000
% 17.05/3.11 % Success case prop preproc time : 0.000
% 17.05/3.11 % Success case prop encoding time : 0.000
% 17.05/3.11 % Success case prop solver time : 0.000
% 17.05/3.11 % Current number of processed clauses : 1368
% 17.05/3.11 % Positive orientable unit clauses : 314
% 17.05/3.11 % Positive unorientable unit clauses: 22
% 17.05/3.11 % Negative unit clauses : 218
% 17.05/3.11 % Non-unit-clauses : 814
% 17.05/3.11 % Current number of unprocessed clauses: 38488
% 17.05/3.11 % ...number of literals in the above : 119055
% 17.05/3.11 % Current number of archived formulas : 0
% 17.05/3.11 % Current number of archived clauses : 1284
% 17.05/3.11 % Clause-clause subsumption calls (NU) : 419625
% 17.05/3.11 % Rec. Clause-clause subsumption calls : 175205
% 17.05/3.11 % Non-unit clause-clause subsumptions : 1010
% 17.05/3.11 % Unit Clause-clause subsumption calls : 7396
% 17.05/3.11 % Rewrite failures with RHS unbound : 0
% 17.05/3.11 % BW rewrite match attempts : 2190
% 17.05/3.11 % BW rewrite match successes : 655
% 17.05/3.11 % Condensation attempts : 0
% 17.05/3.11 % Condensation successes : 0
% 17.05/3.11 % Termbank termtop insertions : 1186553
% 17.05/3.11 % Search garbage collected termcells : 3176
% 17.05/3.11
% 17.05/3.11 % -------------------------------------------------
% 17.05/3.11 % User time : 2.319 s
% 17.05/3.11 % System time : 0.082 s
% 17.05/3.11 % Total time : 2.401 s
% 17.05/3.11 % Maximum resident set size: 6384 pages
% 17.05/3.11
% 17.05/3.11 % -------------------------------------------------
% 17.05/3.11 % User time : 11.609 s
% 17.05/3.11 % System time : 0.373 s
% 17.05/3.11 % Total time : 11.982 s
% 17.05/3.11 % Maximum resident set size: 5888 pages
% 17.05/3.11 % E exiting
%------------------------------------------------------------------------------