%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV693-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:19:17 PM UTC 2026
% Result : Unsatisfiable 4.84s 1.45s
% Output : Refutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 36 ( 19 unt; 2 def)
% Number of atoms : 60 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 22 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 7 con; 0-5 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f61,axiom,
! [X0] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),hAPP(c_Suc,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
fof(f264,axiom,
! [X0,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X0),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
fof(f594,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,X0),X2))
| ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1185,axiom,
! [X2,X3,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X0),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X0),tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(c_lessequals(X2,X0),X3))
| ~ hBOOL(hAPP(c_lessequals(X1,X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
fof(f1307,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_0) ).
fof(f1316,axiom,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X0),X1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
fof(f1390,axiom,
! [X0] : c_SetInterval_Oord__class_OatLeastLessThan(X0,hAPP(c_Suc,X0),tc_nat) = c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__singleton_0) ).
fof(f1391,plain,
! [X0] : c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X0,hAPP(c_Suc,X0),tc_nat),
inference(reorient_equations,[],[f1390]) ).
fof(f1563,axiom,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f1573,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1617,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1619,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1733,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_OatLeastLessThan(hAPP(c_Suc,v_i),v_n,tc_nat),tc_fun(tc_nat,tc_bool))),
inference(forward_demodulation,[],[f1573,f1316]) ).
fof(f1734,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_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_i),v_n,tc_nat),c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool))),
inference(forward_demodulation,[],[f1733,f1563]) ).
fof(f1735,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_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_i),v_n,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(v_i,hAPP(c_Suc,v_i),tc_nat),tc_fun(tc_nat,tc_bool))),
inference(forward_demodulation,[],[f1734,f1391]) ).
fof(f1736,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_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))),
inference(forward_demodulation,[],[f1735,f1563]) ).
fof(f1752,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))
| ~ class_Orderings_Olinorder(tc_nat)
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,v_i),tc_nat),v_n))
| ~ hBOOL(hAPP(c_lessequals(v_i,tc_nat),hAPP(c_Suc,v_i))) ),
inference(superposition,[],[f1736,f1185]) ).
fof(f1755,plain,
( ~ class_Orderings_Olinorder(tc_nat)
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,v_i),tc_nat),v_n))
| ~ hBOOL(hAPP(c_lessequals(v_i,tc_nat),hAPP(c_Suc,v_i))) ),
inference(trivial_inequality_removal,[],[f1752]) ).
fof(f1756,plain,
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,v_i),tc_nat),v_n))
| ~ hBOOL(hAPP(c_lessequals(v_i,tc_nat),hAPP(c_Suc,v_i))) ),
inference(forward_subsumption_resolution,[],[f1755,f1617]) ).
fof(f1767,definition,
( spl0_1
<=> hBOOL(hAPP(c_lessequals(v_i,tc_nat),hAPP(c_Suc,v_i))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1769,plain,
( ~ hBOOL(hAPP(c_lessequals(v_i,tc_nat),hAPP(c_Suc,v_i)))
| spl0_1 ),
inference(avatar_component_clause,[],[f1767]) ).
fof(f1771,definition,
( spl0_2
<=> hBOOL(hAPP(c_lessequals(hAPP(c_Suc,v_i),tc_nat),v_n)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1773,plain,
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,v_i),tc_nat),v_n))
| spl0_2 ),
inference(avatar_component_clause,[],[f1771]) ).
fof(f1774,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1756,f1771,f1767]) ).
fof(f1813,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| spl0_2 ),
inference(resolution,[],[f1773,f264]) ).
fof(f1834,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f1813,f1307]) ).
fof(f1835,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1834]) ).
fof(f1841,plain,
( ~ class_Orderings_Oorder(tc_nat)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),hAPP(c_Suc,v_i)))
| spl0_1 ),
inference(resolution,[],[f1769,f594]) ).
fof(f1850,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),hAPP(c_Suc,v_i)))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f1841,f1619]) ).
fof(f1861,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f1850,f61]) ).
fof(f1862,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1861]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1774]) ).
cnf(s12,plain,
spl0_2,
inference(sat_conversion,[],[f1835]) ).
cnf(s20,plain,
spl0_1,
inference(sat_conversion,[],[f1862]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s12,s20]) ).
fof(f1863,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV693-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 12:16:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.84/1.45 % (749501)Input is clausal, will run a generic CNF schedule.
% 4.84/1.45 % (749506)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4274708474:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.84/1.45 % (749507)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1092785398:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.84/1.45 % (749509)lrs+10_1_sil=8000:sp=occurrence:random_seed=469492017:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.84/1.45 % (749510)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4289940316:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.84/1.45 % (749511)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3088722188:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.84/1.45 % (749508)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=861137799:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.84/1.45 % (749512)dis-21_1_sil=8000:lcm=predicate:random_seed=3599106440:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.84/1.45 % (749510)Instruction limit reached!
% 4.84/1.45 % (749510)------------------------------
% 4.84/1.45 % (749510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.45 % (749510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.45 % (749510)CaDiCaL version: 2.1.3
% 4.84/1.45 % (749510)Termination reason: Instruction limit
% 4.84/1.45 % (749510)Termination phase: Saturation
% 4.84/1.45 % (749510)Time elapsed: 0.066 s
% 4.84/1.45 % (749510)Peak memory usage: 89 MB
% 4.84/1.45 % (749510)Instructions burned: 114 (million)
% 4.84/1.45 % (749512)Instruction limit reached!
% 4.84/1.45 % (749512)------------------------------
% 4.84/1.45 % (749512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.45 % (749512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.45 % (749512)CaDiCaL version: 2.1.3
% 4.84/1.45 % (749512)Termination reason: Instruction limit
% 4.84/1.45 % (749512)Termination phase: Saturation
% 4.84/1.45 % (749512)Time elapsed: 0.066 s
% 4.84/1.45 % (749512)Peak memory usage: 90 MB
% 4.84/1.45 % (749512)Instructions burned: 118 (million)
% 4.84/1.45 % (749509)Instruction limit reached!
% 4.84/1.45 % (749509)------------------------------
% 4.84/1.45 % (749509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.45 % (749509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.45 % (749509)CaDiCaL version: 2.1.3
% 4.84/1.45 % (749509)Termination reason: Instruction limit
% 4.84/1.45 % (749509)Termination phase: Saturation
% 4.84/1.45 % (749509)Time elapsed: 0.067 s
% 4.84/1.45 % (749509)Peak memory usage: 89 MB
% 4.84/1.45 % (749509)Instructions burned: 107 (million)
% 4.84/1.45 % (749511)Instruction limit reached!
% 4.84/1.45 % (749511)------------------------------
% 4.84/1.45 % (749511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.45 % (749511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.45 % (749511)CaDiCaL version: 2.1.3
% 4.84/1.45 % (749511)Termination reason: Instruction limit
% 4.84/1.45 % (749511)Termination phase: Saturation
% 4.84/1.45 % (749511)Time elapsed: 0.109 s
% 4.84/1.45 % (749511)Peak memory usage: 90 MB
% 4.84/1.45 % (749511)Instructions burned: 181 (million)
% 4.84/1.45 % (749522)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3568364694:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 4.84/1.45 % (749520)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3660356702:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 4.84/1.45 % (749521)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1802958232:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 4.84/1.45 % (749520)Refutation not found, incomplete strategy
% 4.84/1.45 % (749520)------------------------------
% 4.84/1.45 % (749520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.45 % (749520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.45 % (749520)CaDiCaL version: 2.1.3
% 4.84/1.45 % (749520)Termination reason: Refutation not found, incomplete strategy
% 4.84/1.45 % (749520)Time elapsed: 0.043 s
% 4.84/1.45 % (749520)Peak memory usage: 90 MB
% 4.84/1.45 % (749520)Instructions burned: 74 (million)
% 4.84/1.45 % (749523)lrs+10_64_to=lpo:sil=8000:random_seed=2326387880:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.84/1.45 % (749522)First to succeed.
% 4.84/1.45 % (749522)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-749501"
% 4.84/1.45 % (749521)Instruction limit reached!
% 4.84/1.45 % (749521)------------------------------
% 4.84/1.45 % (749521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.45 % (749521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.45 % (749521)CaDiCaL version: 2.1.3
% 4.84/1.45 % (749521)Termination reason: Instruction limit
% 4.84/1.45 % (749521)Termination phase: Saturation
% 4.84/1.45 % (749521)Time elapsed: 0.101 s
% 4.84/1.45 % (749521)Peak memory usage: 91 MB
% 4.84/1.45 % (749521)Instructions burned: 191 (million)
% 4.84/1.45 % (749523)Instruction limit reached!
% 4.84/1.45 % (749523)------------------------------
% 4.84/1.45 % (749523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.45 % (749523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.45 % (749523)CaDiCaL version: 2.1.3
% 4.84/1.45 % (749523)Termination reason: Instruction limit
% 4.84/1.45 % (749523)Termination phase: Saturation
% 4.84/1.45 % (749523)Time elapsed: 0.075 s
% 4.84/1.45 % (749523)Peak memory usage: 90 MB
% 4.84/1.45 % (749523)Instructions burned: 126 (million)
% 4.84/1.45 % (749528)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3491966833:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 4.84/1.45 % (749506)Also succeeded, but the first one will report.
% 4.84/1.45 % (749529)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=778161197:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 4.84/1.45 % (749520)------------------------------
% 4.84/1.45 % (749520)------------------------------
% 4.84/1.45 % (749522)Refutation found. Thanks to Tanya!
% 4.84/1.45 % SZS status Unsatisfiable for theBenchmark
% 4.84/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 5.66/1.65 % (749522)------------------------------
% 5.66/1.65 % (749522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.65 % (749522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.65 % (749522)CaDiCaL version: 2.1.3
% 5.66/1.65 % (749522)Termination reason: Refutation
% 5.66/1.65 % (749522)Time elapsed: 0.051 s
% 5.66/1.65 % (749522)Peak memory usage: 92 MB
% 5.66/1.65 % (749522)Instructions burned: 93 (million)
% 5.66/1.65 % (749522)------------------------------
% 5.66/1.65 % (749522)------------------------------
% 5.66/1.65 % (749501)Success in time 0.779 s
% 5.66/1.65 % Vampire exiting
%------------------------------------------------------------------------------