%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV693-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 09:08:58 AM UTC 2026
% Result : Unsatisfiable 25.57s 8.80s
% Output : CNFRefutation 25.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 18 unt; 0 def)
% Number of atoms : 30 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-5 aty)
% Number of variables : 15 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(c_662,plain,
class_Orderings_Olinorder(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
fof(cls_conjecture_0,axiom,
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('theBenchmark.p',cls_conjecture_0) ).
cnf(c_689,plain,
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(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_690,plain,
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))) != 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)),
inference(copy,[status(thm)],[c_689]) ).
fof(cls_CHAINED_0,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_691,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_ivl__disj__un_I3_J_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(VAR_1,VAR_0),VAR_2))
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(VAR_1,c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),VAR_0),c_SetInterval_Oord__class_OgreaterThanLessThan(VAR_1,VAR_2,VAR_0),tc_fun(VAR_0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_ivl__disj__un_I3_J_0) ).
cnf(c_790,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C))
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),c_SetInterval_Oord__class_OgreaterThanLessThan(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_ivl__disj__un_I3_J_0]) ).
fof(cls_atLeastLessThan__singleton_0,axiom,
! [VAR_0] : c_SetInterval_Oord__class_OatLeastLessThan(VAR_0,hAPP(c_Suc,VAR_0),tc_nat) = c_Set_Oinsert(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
file('theBenchmark.p',cls_atLeastLessThan__singleton_0) ).
cnf(c_796,plain,
c_SetInterval_Oord__class_OatLeastLessThan(A,hAPP(c_Suc,A),tc_nat) = c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
inference(clausify,[status(thm)],[cls_atLeastLessThan__singleton_0]) ).
cnf(c_797,plain,
c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(A,hAPP(c_Suc,A),tc_nat),
inference(copy,[status(thm)],[c_796]) ).
fof(cls_atLeastSucLessThan__greaterThanLessThan_0,axiom,
! [VAR_0,VAR_1] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,VAR_0),VAR_1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(VAR_0,VAR_1,tc_nat),
file('theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
cnf(c_834,plain,
c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,A),B,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat),
inference(clausify,[status(thm)],[cls_atLeastSucLessThan__greaterThanLessThan_0]) ).
cnf(c_835,plain,
c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,A),B,tc_nat),
inference(copy,[status(thm)],[c_834]) ).
cnf(c_2564,plain,
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_SetInterval_Oord__class_OatLeastLessThan(v_i,hAPP(c_Suc,v_i),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))) != 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)),
inference(paramod,[status(thm)],[c_797,c_690]) ).
cnf(c_2146,plain,
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_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))) != 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)),
inference(paramod,[status(thm)],[c_835,c_2564]) ).
cnf(c_2565,plain,
( 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_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolve,[status(thm)],[c_790,c_691]) ).
cnf(c_2566,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(v_i,hAPP(c_Suc,v_i),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramod,[status(thm)],[c_797,c_2565]) ).
cnf(c_2567,plain,
( 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_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramod,[status(thm)],[c_835,c_2566]) ).
cnf(c_2562,plain,
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_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat),
inference(resolve,[status(thm)],[c_662,c_2567]) ).
cnf(c_2568,plain,
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_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)),
inference(paramod,[status(thm)],[c_2562,c_2146]) ).
cnf(c_2563,plain,
$false,
inference(copy,[status(thm)],[c_2568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV693-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.40 % Computer : n016.cluster.edu
% 0.11/5.40 % Model : x86_64 x86_64
% 0.11/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.40 % Memory : 8046.5625MB
% 0.11/5.40 % OS : Linux 6.8.0-71-generic
% 0.11/5.40 % CPULimit : 300
% 0.11/5.40 % WCLimit : 300
% 0.11/5.40 % DateTime : Sat Sep 26 14:52:21 UTC 2026
% 0.11/5.41 % CPUTime :
% 0.11/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.41 % Process 1127700 was started by sandbox on n016,
% 0.11/5.41 % Sat Sep 26 14:52:21 2026
% 0.11/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.47
% 0.11/5.47 % From the command line: assign(max_seconds, 300).
% 25.57/8.80
% 25.57/8.80 % SZS status Unsatisfiable for theBenchmark
% 25.57/8.80
% 25.57/8.80 % Proof 1 at 3.24 (+ 0.06) seconds.
% 25.57/8.80 % Length of proof is 12.
% 25.57/8.80 % Level of proof is 3.
% 25.57/8.80 % Maximum clause weight is 348.000.
% 25.57/8.80 % Given clauses 192.
% 25.57/8.80
% 25.57/8.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------